# Past seminars in 2020/21 and 2021/22

• ### 11/05: Benedikt Kloss (Flatiron)

Abstract: Whether many-body localization (MBL) can exist in one-dimensional systems with local interactions in the absence of quenched disorder is an open question. Recently, interacting systems in a tilted field have emerged as a candidate to exhibit MBL-like behaviour. In this talk I will provide a thorough numerical analysis of this proposition. In particular, I will discuss the role of an additional discrete symmetry in the case of a purely linear field and its implications for localization.

• ### 04/05: Miguel Frías-Pérez (MPG)

Abstract: I will present a new family of Markov chains based on tensor network contractions, and demonstrate that it allows to greatly mitigate some of the limitations of more traditional approaches, such as slow convergence in presence of competing interactions. Results of the application of the method for the two and three dimensional Ising model will be shown, along with some preliminary results on continuous models.

• ### 27/04: Romain Vasseur (UMass Amherst)

Abstract: Monitored quantum circuits (MRCs) exhibit a measurement-induced phase transition between area-law and volume-law entanglement scaling as a function of the measurement rate. In this talk, I will first review our understanding of such measurement-induced phase transitions. I will argue that MRCs with a conserved charge additionally exhibit two distinct volume-law entangled phases that cannot be characterized by equilibrium notions of symmetry-breaking or topological order, but rather by the non-equilibrium dynamics and steady-state distribution of charge fluctuations. These include a charge-fuzzy phase in which charge information is rapidly scrambled leading to Luttinger-liquid-like spatial fluctuations of charge in the steady state, and a charge-sharp phase in which measurements collapse quantum fluctuations of charge without destroying the volume-law entanglement of neutral degrees of freedom. I will present some statistical mechanics and effective field theory approaches to such charge-sharpening transitions.

• ### 13/04: Lei Ying (Zhejiang)

Abstract: Quantum many-body scarring (QMBS), as a novel coherent state mitigating the quantum thermalization, exhibits potential applications in quantum information. As yet, existing experimental realizations of the QMBS are based on kinetically-constrained systems, realized on atomic platforms. In this talk, we will introduce a distinct kind of QMBS states by approximately decoupling a part of the many-body Hilbert space in the computational basis. Utilizing a programmable superconducting processor with 30 qubits and 29 tunable couplings, we realize such a Hilbert space scarring in a non-constrained model with different lattice geometries, including a linear chain as well as a quasi-one-dimensional comb configuration. We provide direct evidence for QMBS states by measuring qubit population dynamics, quantum fidelity and entanglement entropy. Our experimental findings broaden the realm of QMBS mechanisms and pave the way to exploiting correlations in QMBS states for applications in quantum information technology. References: arXiv:2201.03438v2.

• ### 13/04: Silvia Pappalardi (ENS Paris)

Abstract: In the past few years, there has been considerable activity around a set of quantum bounds on transport coefficients (viscosity, conductivity) and chaos (Lyapunov exponents), relevant at low temperatures. The interest comes from the fact that black-hole models seem to saturate all of them. However, the relation between the different bounds and physical properties of the systems saturating the is still a matter of ongoing research.

In this talk, I will discuss how one can gain physical intuition by studying classical and quantum free dynamics on curved manifolds. Thanks to the curvature, such models display chaotic dynamics up to low temperatures and – as I will show how- they violate the bounds in the classical limit.
The talk aims to discuss three different ways in which quantum effects arise to enforce the bounds in practice. For instance, I will show how chaotic behaviour is limited by the quantum effects of the curvature itself. As an illustrative example, I will consider the simple case of a free particle on a two-dimensional manifold, constructed by joining the surface of constant negative curvature — a paradigmatic model of quantum chaos — to a cylinder. The resulting phenomenology can be generalized to the case of several (constant) curvatures. The presence of a hierarchy of length scales enforces the bound to chaos up to zero temperature.

* Pappalardi, Kurchan, Low temperature quantum bounds on simple models, arXiv:2106.13269, (2021).

• ### 23/03: Sarang Gopalakrishnan (Penn State)

Title: Diffusion

I will describe a spacetime-duality-based approach to access the spectral statistics of quantum many-body systems. The approach can be applied to generic systems in discrete time but in general it can be pushed to the end only with the aid of numerical computations. In certain cases, however, it leads to exact analytical results. I will describe two classes of local quantum circuits where this can indeed be done: dual-unitary circuits and strongly localising circuits. I will show that these two classes of circuit systems can be respectively considered minimal realisations of chaotic and localised quantum many-body systems.

• ### 23/03: Bruno Bertini (Nottingham)

Title: Duality Approach to the Spectral Statistics

I will describe a spacetime-duality-based approach to access the spectral statistics of quantum many-body systems. The approach can be applied to generic systems in discrete time but in general it can be pushed to the end only with the aid of numerical computations. In certain cases, however, it leads to exact analytical results. I will describe two classes of local quantum circuits where this can indeed be done: dual-unitary circuits and strongly localising circuits. I will show that these two classes of circuit systems can be respectively considered minimal realisations of chaotic and localised quantum many-body systems.

• ### 09 February, 3pm UK time: Guoxian Su (Heidelberg)

Title: Quantum simulation of thermalization dynamics: from lattice gauge theory to many-body scars

Abstract: Advances in quantum simulation have enabled experimental investigation of novel phases of matter. In particular, ultracold atoms in optical lattices present an ideal platform for simulating the physics of strongly correlated quantum many-body systems. In the first part of this talk, I will present the realization of a U(1) lattice gauge theory in a Bose–Hubbard quantum simulator. We investigate the emergent thermal equilibrium by quenching from various initial states and observe the subsequent gauge-invariant dynamics. We demonstrate the effective loss of information as different initial states with the same conserved quantity approach a common steady-state predicted by the thermal ensemble. In the second part, we study the slowed thermalization dynamics with many-body scars in the quantum simulator. We realize many-body scarring by emulating the PXP model with the tilted Bose-Hubbard model and demonstrate unconventional scarring in the presence of detuning potential. By fine-tuning the periodic driving parameters, we show the many-body system can retain initial state information well beyond experimentally accessible times. Our work establishes new realms for studying non-equilibrium phenomena in complex quantum systems and paves the way for exploring more complex thermalization dynamics on synthetic quantum matter devices.

• ### 02 March, 3pm UK time: Thomas Bilitewski (Colorado)

In this talk I will discuss many-body phenomena of topical interest using the lens of classical spin systems. I will begin with results on classical out-of-time ordered correlators (OTOC’s) in a chaotic spin liquid. I will demonstrate the persistence of chaos down to T=0, together with the emergence of the ballistic propagation of a perturbation in a system without well-defined spin-waves To quantify the chaos in this system I will use the butterfly speed and the Lyapunov exponent characterising the spread and growth of the OTOC’s, and discuss their temperature scaling. I will then discuss how this phenomenology is changed in the presence of thermal phase transitions, where a symmetry is broken and (ballistic) quasi-particles/spin-waves emerge that subsume the chaotic butterfly speed found in the paramagnetic spin-liquid. Bonus: time-permitting I will discuss recent results on long-time anomalous hydrodynamics/scaling in the classical 1D Heisenberg chain based on Phys. Rev. Lett. 121, 250602 (2018),Phys. Rev. B 103, 174302 (2021), arxiv:2108.11964

• ### 02 February, 3pm UK time: Netanel Lindner (Technion)

Topology and Dynamical Liquid Crystallinity in Many-Body Floquet Systems “Floquet engineering” of band structures through the application of coherent time-periodic drives – has recently emerged as a powerful tool for creating new types of topological phases. We show that this tool can also be used to induce non-equilibrium correlated states with dynamical spontaneously broken symmetry. In particular, we study lightly doped semiconductors driven by a resonant driving field. We show that such a system can spontaneously develop quantum liquid crystalline order featuring extreme anisotropy whose directionality rotates as a function of time. The phase transition to this correlated state occurs in the steady state of the system achieved due to the interplay between the coherent external drive, electron-electron interactions, and dissipative processes arising from the coupling to phonons and the electromagnetic environment. Our results demonstrate how Floquet engineering can be used to induce novel non-equilibrium phases exhibiting an interplay of topology and dynamical symmetry breaking.

• ### 26 January, 3pm UK time: Pietro Brighi (IST Austria)

Title: Propagation of many-body localization in an Anderson insulator

Abstract: In this talk, I will present our recent work on the interplay of many-body localized (MBL) systems and small baths. Recently, the fate of localized particles when coupled to a small thermalizing system, viewed as a quantum bath, received significant attention both theoretically and experimentally. In this work, we discuss the smallest possible quantum bath, consisting of a single mobile impurity, interacting locally with an Anderson insulator with finite particle density. Through perturbative arguments, we provide an approximate framework where localization is stable against the effect of the thermalizing particle. Next, we analyze the dynamics of the system both in an approximate time-dependent Hartree picture and through the quasi-exact time-evolving-block-decimation (TEBD). While the approximate dynamics, ignoring entanglement among the two particle species, results in late-time thermalization, the full dynamics presents sound evidence of localization. We further develop a phenomenological picture based on the localization of the mobile particle, predicting that the impurity turns the previously non-interacting Anderson insulator into an MBL phase, giving rise to non-trivial entanglement patterns in good agreement with the numerical simulations. Finally, we use an extension of the density-matrix renormalization group (DMRG) algorithm to highly excited states to sample the middle of the spectrum. Through the study of observables and entanglement in the highly excited eigenstates we confirm the picture introduced in the dynamics.  Dynamics and the DMRG-X results provide compelling evidence for the stability of localization.References:  arXiv:2109.07332, arXiv:2111.08603.

• ### 24 November, 3pm UK time: Balázs Pozsgay (Eötvös Loránd University)

Title: Lindblad equations with Yang-Baxter integrability

Abstract: The Yang-Baxter equation is one of the cornerstones of integrability, it leads to a canonical framework for the construction of integrable spin chains and other models. In the last 5 years interest also turned towards Lindblad systems, and the question was asked, whether there are integrable Lindblad equations with an underlying Yang-Baxter structure. The Lindblad equation describes coupling with an environment, including losses or external driving, and it is a linear equation for the density matrix. In this talk we show that there are indeed Yang-Baxter integrable Lindblad systems. We focus on quantum spin chains, and give examples including the first such system found by Essler and Prosen. Afterwards we explain our recent work which shows how to find/construct such integrable equations from scratch.

• ### 17 November, 3pm UK time: Michael Knap (TUM)

Title: Anomalous transport and operator growth in constrained quantum matter
Abstract: The far from equilibrium dynamics of generic interacting quantum systems is characterized by a handful of universal guiding principles, among them the diffusive transport of globally conserved quantities and the ballistic spreading of initial local operators. Here, we discuss that in certain constrained many-body systems the structure of conservation laws can cause a drastic modification of this universal behavior. In particular, we focus on a dipole conserving “fracton” chain which exhibits a localization transition, separating an ergodic dynamical phase from a frozen one. Even in the ergodic phase, transport is anomalously slow and exhibits subdiffusive scaling. We explain this finding by a developing general hydrodynamical model, that yields an accurate description of the scaling form of charge correlation functions. Furthermore, we investigate the operator growth characterized by out-of-time correlations functions (OTOCs) in this dipole conserving system. We identify a critical point, tied to the underlying localization transition, with unconventional sub-ballistically moving OTOC front. We use the scaling properties at the critical point to derive an effective description of the moving operator front via a biased random walk with long waiting times and support. Our arguments are supported numerically by classically stimulable automaton circuits.J. Feldmeier, P. Sala, G. de Tomasi, F. Pollmann, MK, PRL 125, 245303 (2020).

• ### 10 November, 3pm UK time: Jiri Minar (Amsterdam)

Title: Disorder enhanced quantum many-body scars in Hilbert hypercubes

Abstract: I will start by discussing the role of phonons in lattice Rydberg gases and how they can be exploited to engineer various lattice spin models with realistic (correlated) disorder. I will then focus specifically on a model arising in facilitated Rydberg chains, which features a Hilbert space with the topology of a d-dimensional hypercube. This allows for a straightforward interpretation of the many-body dynamics in terms of a single-particle one on the Hilbert space and provides an explicit link between the many-body and single-particle scars. Exploiting this perspective, we show that an integrability-breaking disorder enhances the scars followed by inhibition of the dynamics due to strong localization of the eigenstates in the large disorder limit. Additionally, mapping the model to the spin-1/2 XX Heisenberg chain offers a geometrical perspective on the recently proposed Onsager scars [Phys. Rev. Lett. 124, 180604 (2020)], which can be identified with the scars on the edge of the Hilbert space.

Based on: arXiv:1607.06295, arXiv:1802.00379, arXiv:2012.05310

• ### 3 November, 3pm UK time: Pieter Claeys (Cambridge)

Title: Absence of superdiffusion in certain random spin models
Abstract: The dynamics of spin at finite temperature in the spin-1/2 Heisenberg chain was found to be superdiffusive in numerous recent numerical and experimental studies. Theoretical approaches to this problem have emphasized the role of nonabelian SU(2) symmetry as well as integrability, but the associated methods cannot be readily applied when integrability is broken. After an introduction to superdiffusion I will examine spin transport in such a spin-1/2 chain in which the exchange couplings fluctuate in space and time, breaking integrability but not spin symmetry, showing that operator dynamics in the strong noise limit can be analyzed using conventional perturbation theory. I will argue that the spin dynamics undergo enhanced diffusion with some interesting transient behavior rather than superdiffusion, comparing the dynamics with both a hydrodynamic approach and tensor network simulations. Based on arXiv:2110.06951

• ### 27 October, 3pm UK time: Yves Ywan (Oxford)

Title: Beyond the Freshman’s Dream: Classical fractal spin liquids from matrix cellular automata in three-dimensional lattice models

Abstract: We consider disorder-free Hamiltonians consisting of three-body Ising interactions on two realistic 3D lattices: trillium and hyperhyperkagome. Like the well-studied 2D Newman-Moore (NM) model, our 3D models possess trivial thermodynamics but exhibit ‘fragile’ glassy dynamics arising from the hierarchical and immobile nature of the low-energy excitations. Unlike the NM model, the structure of the ground state and its excitations cannot be described by scalar cellular automata (CA). Instead, we show how matrix CAs provide the necessary language to understand the fractal symmetries and ‘fractons’ present in our 3D models. We comment on the introduction of quantum fluctuations introduced by a transverse magnetic field. This talk is based on arXiv:2109.06207.

• ### 20 October, 3pm UK time: Katja Klobas (Oxford)

Title: Exact thermalization dynamics in the “Rule 54” Quantum Cellular Automaton

Abstract: When a generic isolated quantum many-body system is driven out of equilibrium, its local properties are eventually described by the thermal ensemble. This picture can be intuitively explained by saying that, in the thermodynamic limit, the system acts as a bath for its own local subsystems. Despite the undeniable success of this paradigm, for interacting systems most of the evidence in support of it comes from numerical computations in relatively small systems, and there are very few exact results. In the talk, I will present an exact solution for the thermalization dynamics in the “Rule 54” cellular automaton, which can be considered the simplest interacting integrable model. After introducing the model and its tensor-network formulation, I will present the main tool of my analysis: the space-like formulation of the dynamics. Namely, I will recast the time-evolution of finite subsystems in terms of a transfer matrix in space and construct its fixed-points. I will conclude by showing two examples of physical applications: dynamics of local observables and entanglement growth. The talk is based on a recent series of papers: arXiv:2012.12256,arXiv:2104.04511, and arXiv:2104.04513.

• ### 13 October, 3pm UK time: Andrea De Luca (CNRS)

Title: Universal out-of-equilibrium dynamics of 1D noisy critical quantum systems

Abstract: We consider critical one dimensional quantum systems initially prepared in their groundstate and perturbed by a smooth noise coupled to the energy density. By using conformal field theory, we deduce a universal description of the out-of-equilibrium dynamics. In particular, the full time-dependent distribution of any 2-pt chiral correlation function can be obtained from solving two coupled ordinary stochastic differential equations. In contrast with the general expectation of heating, we demonstrate that the system reaches a non-trivial and universal stationary state characterized by broad distributions. As an example, we analyse the local energy density: while its first moment diverges exponentially fast in time, the stationary distribution, which we derive analytically, is symmetric around a negative median and exhibits a fat tail with 3/2 decay exponent. We obtain a similar result for the entanglement entropy production associated to a given interval of size L. The corresponding stationary distribution has a 3/2 right tail for all L, and converges to a one-sided Levy stable for large L.

• ### 06 October, 3pm UK time: Adam Smith (Nottingham)

Title:  Identifying Correlation Clusters in Many-Body Localized Systems

Abstract:  We introduce techniques for analysing the structure of quantum states of many-body localized (MBL) spin chains by identifying correlation clusters from pairwise correlations. These techniques proceed by interpreting pairwise correlations in the state as a weighted graph, which we analyse using an established graph theoretic clustering algorithm. We validate our approach by studying the eigenstates of a disordered XXZ spin chain across the MBL to ergodic transition, as well as the non-equilibrium dynamics in the MBL phase following a global quantum quench. We successfully reproduce theoretical predictions about the MBL transition obtained from renormalization group schemes. Furthermore, we identify a clear signature of many-body dynamics analogous to the logarithmic growth of entanglement. The techniques that we introduce are computationally inexpensive and in combination with matrix product state methods allow for the study of large scale localized systems. Moreover, the correlation functions we use are directly accessible in a range of experimental settings including cold atoms.

Reference: arXiv:2108.03251

• ### 29 September, 3pm UK time: Spyros Sotiriadis (FU Berlin/Crete)

Signatures of Chaos in Non-integrable Models of Quantum Field Theory

Abstract: Despite the growing interest in the study of quantum chaos in many-body systems, numerical tests of chaoticity signatures, like spectral statistics, are almost exclusively limited to lattice models, leaving continuous models largely unexplored. Among them relativistic Quantum Field Theories (QFTs) and their dynamics lie at the cornerstone of important open questions of theoretical physics, like the black hole information paradox, making the study of ergodicity in QFT a topic of fundamental interest. Here we study signatures of quantum chaos in (1+1)D QFTs and show that, even though their level spacing statistics agree with the predictions of Random Matrix Theory, on the contrary, their eigenvector components follow a distribution markedly different from the expected Gaussian, raising questions on the validity of the Eigenstate Thermalisation Hypothesis in these models. To derive and validate our results we push the limits of the numerical method of Hamiltonian truncation beyond earlier studies and devise strict measures of the truncation error.
• ### 22 September, 3pm UK time: Ivan Khaymovich (MPI-PKS Dresden)

Random-matrix approach to slow dynamics in quantum systems

Abstract: In this talk, we will discuss a random-matrix approach to the description of disordered many-body systems and their Hilbert-space structure, focusing on ergodicity breaking effects and slow dynamics in such models. As a generic example of this approach, we consider the static and the dynamical phases in a Rosenzweig-Porter random matrix ensemble with a distribution of off-diagonal matrix elements of the form of the large-deviation ansatz. We present a general theory of survival probability in such a random-matrix model and show that the averaged survival probability may decay with time as a simple exponent, as a stretch-exponent and as a power-law or slower. Correspondingly, we identify the exponential, the stretch-exponential and the frozen-dynamics phases. We consider the mapping of the Anderson localization model on Random Regular Graph, the known proxy of MBL, onto the RP model and find exact values of the stretch-exponent kappa in the thermodynamic limit. Our theory allows to describe analytically the finite-size multifractality and to compute the critical length with the exponent 1 associated with it.

• ### 9 September, 3pm UK time: Wen Wei Ho, Gordon and Betty Moore Postdoctoral Fellow, Harvard University

Title: Interacting Phases of Matter protected by Multiple Time-Translation Symmetries in Quasiperiodically-driven Systems

Abstract: The discrete time-translation symmetry of a periodically-driven (Floquet) system allows for the existence of novel, nonequilibrium interacting phases of matter. A well-known example is the Discrete Time Crystal, a phase distinguished by the spontaneous breaking of this time-translation symmetry. In this talk, I will explain how quasiperiodically-driven systems, that is, systems driven with two or more incommensurate frequencies, possess a notion of *multiple* time-translation symmetries. This in turn leads to the possibility of realizing a panoply of novel nonequilibrium phases of matter characterized by such symmetries, both spontaneous symmetry-breaking (“discrete time quasi-crystals”) and topological. I will demonstrate that these phases are stable in a long-lived, ‘preheating’ regime, by outlining rigorous mathematical results establishing slow heating at high driving frequencies. These new nonequilibrium phases can readily be realized in quantum simulator platforms of today.

• ### 16 September, 3pm UK time: David Luitz, MPIPKS Dresden

Title: Hierarchy of Relaxation Timescales in Local Random Liouvillians

Abstract: To characterize the generic behavior of open quantum systems, we consider random, purely dissipative Liouvillians with a notion of locality. We find that the positivity of the map implies a sharp separation of the relaxation timescales according to the locality of observables. Specifically, we analyze a spin-1/2 system of size ℓ with up to n-body Lindblad operators, which are n local in the complexity-theory sense. Without locality (n=ℓ), the complex Liouvillian spectrum densely covers a “lemon”-shaped support, in agreement with recent findings [S. Denisov et al., Phys. Rev. Lett. 123,140403(2019)]. However, for local Liouvillians (n<ℓ), we find that the spectrum is composed of several dense clusters with random matrix spacing statistics, each featuring a lemon-shaped support wherein all eigenvectors correspond to n-body decay modes. This implies a hierarchy of relaxation timescales of n-body observables, which we verify to be robust in the thermodynamic limit. Our findings for n locality generalize immediately to the case of spatial locality, introducing further splitting of timescales due to the additional structure.

• ### 7 October, 3pm UK time: Tom Iadecola, Iowa State University

Title: Nonergodic Quantum Dynamics from Deformations of Classical Cellular Automata

Abstract: Classical reversible cellular automata (CAs), which describe the discrete-time dynamics of classical degrees of freedom in a finite state-space, can exhibit exact, nonthermal quantum eigenstates despite being classically chaotic. We show that families of periodically-driven (Floquet) quantum dynamics that include a classical CA in a special limit retain certain nonthermal eigenstates of the CA. These dynamics are nonergodic in the sense that certain product states on a periodic classical orbit fail to thermalize, while generic initial states thermalize as expected in a quantum chaotic system. We demonstrate that some signatures of these effects can be probed in quantum simulators based on Rydberg atoms in the blockade regime. These results establish classical CAs as parent models for a class of quantum chaotic systems with rare nonthermal eigenstates.

### Title: Probing the onset of quantum chaos through eigenstate deformations

Abstract: In this talk I will discuss our recent results on detecting integrability breaking using adiabatic deformations of the system. I will show one can detect the onset of chaos at perturbation strengths much below standard measures of random matrix theory behavior. This intermediate regime, separating ergodic and non-ergodic systems, is characterised by very slow relaxation and enhanced sensitivity to perturbations. Clean and disordered 1D systems will be discussed and the talk will be based on arXiv:2004.05043 and arXiv:2009.04501.

• ### 21 October, 3pm UK time: Olalla Castro Alvaredo, City University

Title: Out-of-Equilibrium Entanglement Dynamics in Quantum Integrable Models

Abstract: In this talk I will discuss the main results of the papers arXiv:2001.10007 andarXiv:1907.11735.  In these papers we studied both analytically and numerically the time dependence of the Rényi and von Neumann entropies in the integrable Ising spin chain, following different kinds of global quenches. We were interested in studying the continuum limit of these theories, namely the associated quantum field theories (QFTs) and we used QFT techniques, particularly, branch point twist fields, to perform our analytical computations. Using these techniques we have gained access not only to the precise leading linear large time dependence of the entropies that is observed in many integrable models but also to oscillatory behaviour that, depending on the quench, can become the leading feature of entanglement, at least for small quenches. Although there is still much to understand in this area of research, one of our conclusions is that the integrability of the quenched model is not the sole feature to determine its entanglement dynamics, in particular, whether or not the entropies will grow linearly with time or exhibit persistent undamped oscillations.

• ### 28 October, 3pm UK time: Alessandro Romito, Lancaster

Measurement induced entanglement transition: from stroboscopic to continuous dynamics

Abstract: Quantum measurements can induce an entanglement transition between extensive and sub-extensive scaling of the entanglement entropy. This transition is of great interest since it illuminates the intricate physics of thermalization and control in open interacting quantum systems. Whilst this transition is well established for stroboscopic measurements in random quantum circuits, a crucial link to physical settings is its extension to continuous observations where, for an integrable model, it has been shown that a sub-extensive scaling appears for arbitrarily weak measurements. In this talk, after reviewing the entanglement transitions for random unitary circuits and projective measurements, I present results for a one-dimensional quantum circuit evolving under random unitary transformations and generic positive operator-valued measurements of “variable strength”. I will show that, for stroboscopic dynamics, there is a consistent phase boundary in the space of the measurement strength and the measurement probability, with a critical value of the measurement strength below which the system is always ergodic. I will further show that the entanglement transition at finite coupling persists for a continuously measured system whose unitary evolution is randomly nonintegrable. These results open the possibility to investigate the measurement induced entanglement transition in quantum architectures accessible via continuous measurements.

• ### 4 November, 3pm UK time: Sthitadhi Roy (Oxford)

Title: Measurement-induced entanglement phase transitions in all-to-all quantum circuits and quantum trees

Abstract: Measurements in the background of an otherwise unitary time-evolution can make a quantum system reside in an entangled or a disentangled phase separated by a measurement-induced entanglement phase transition. I will discuss some aspects of such phase transitions in all-to-all quantum circuits with measurements.  All-to-all models simplify some of the complications arising from spatial structure in low-dimensional systems allowing for some exact results. Exploiting the underlying locally tree-like structure of the space-time graph, we quantify the quantum information flowing through the circuit via the entanglement between the apex and  base of the tree. The tree-like structure of the graph allows for a recursive solution to the problem which is analytically solvable in some cases yielding exact results for the location of the critical point and scaling  near the critical point. Away from these cases, we present numerical results which confirm the universality of our results.

Reference: arXiv:2009.11311

TBA

• ### 19 November, 3pm UK time: Yevgeny Bar Lev (Ben Gurion)

Title: Transport in long-range interacting systems

Yevgeny Bar Lev

Abstract: In generic systems with local interactions transport is diffusive, though it can be supressed by the addition of disorder. Introducing long-range interactions, should intuitively, enhance transport by long-range hop. Using numerically exact techniques I will show that this is not the case for a number of generic one-dimensional systems. All studied systems, for sufficiently short-range interactions, show universal behaviour of asymptotically emergent locality and a unique composite transport comprised of diffusive and superdiffusive features. Introducing disorder, slows down the transport and makes it subdiffusive, similarly to the situation for local systems.

• ### 25 November, 3pm UK time: Remy Dubertrand (Northumbria University)

Many-body semiclassics for Bose-Hubbard:spectral statistics and random wave approach
Semiclassical techniques from quantum chaos have been recently generalised to describe many-body interacting bosonic systems written as second quantised models. To understand the emergence of new phenomena due to many-body coherent effects I will first motivate how to build a quantum/classical correspondence, and how to follow the semiclassical program from there. This will be used first to state when universal spectral appear in Bose-Hubbard models. Then I will explain how to describe the eigenstates using a statistical perspective. This involves more precisely the connection with Random Matrix Theory and Berry’s ansatz of random superpositions of Fock states respectively. In particular it will be discussed how to use it in order to tackle the issue of thermalisation in isolated systems.
• ### 2 December, 3pm UK time: Marin Bukov (Sofia University)

Title: Floquet (Pre-)thermalization in Many-Body Systems away from the High-Frequency Limit

Abstract: We study the dynamics of periodically-driven many-body systems away from the high-frequency regime, and introduce a class of Floquet systems where the notion of prethermalization can be naturally extended to intermediate and low driving frequencies. We investigate numerically the dynamics of both integrable and non-integrable systems, and provide evidence for the formation of a long-lived prethermal plateau, akin to the high-frequency limit, where the system thermalizes with respect to an effective Hamiltonian captured by the inverse-frequency expansion (IFE). However, unlike the high-frequency regime, we find that heating rates can be both power-law or exponentially suppressed, depending on the properties of the drive Hamiltonian. We analyze the stability of the prethermal plateau to small perturbations in the periodic drive, and show that, for systems with power-law suppressed heating, the plateau duration is insensitive to the perturbation strength, in contrast to models with exponentially suppressed heating. Interestingly, any infinitesimal perturbation is enough to restore the ergodic properties of the system and eliminate residual finite-size effects. Although the regime where the Floquet system leaves the prethermal plateau and starts heating up to infinite temperature is not captured by the IFE, we find that the evolved subsystem is described well by a thermal state w.r.t.~the IFE Hamiltonian, with a gradually changing temperature.

• ### 3 February, 3pm UK time: Alexios Michailidis, IST Austria

Quantum scars and slow thermalization in Rydberg blockades

Recent experiments have shown that the relaxation time in Rydberg blockades depends strongly on the initial state. This feature was attributed to a set of atypical eigenstates (quantum scars) of an idealised kinetically constrained model (PXP). I will address the atypical dynamics of PXP-type models in one  and two dimensions using algebraic and variational means [1], and introduce variations of the model which further suppress thermalization [2]. I will propose a time-dependent perturbation to reduce the effects of the previously ignored long-range interactions and present theoretical calculations and experimental observations of the enhancement of coherence in 1D and 2D lattices [3]. Finally, motivated by the time-periodic perturbations I will discuss a novel type of Floquet dynamics based on quantum scars. This model features stable subharmonic response akin to time crystalline behaviour and strong suppression of thermalization for a specific set of initial states.

[1] PRX 10, 011055

[2] PRR 2, 022065

[3] arXiv:2012.12276

• ### 17 February, 3pm UK time: Dr Lev Vidmar (Jozef Stefan Institute)

Ergodicity breaking transition in finite disordered spin chains

We study disorder-induced ergodicity breaking transition in high-energy eigenstates of interacting spin-1/2 chains. We study several ergodicity indicators: the spectral level spacing statistics, the eigenstate entanglement entropy, and the ratio of the Thouless time versus the Heisenberg time. For the latter, we argue that the ergodicity breaking transition in interacting spin chains occurs when both time scales are of the same order, and their ratio becomes a system-size independent constant. Interestingly, we observe that the ergodicity breaking transition in systems studied by exact diagonalization (with around 20 lattice sites) takes place at disorder values lower than those reported in previous works. We discuss the observation that scaled results in finite systems by increasing the system size exhibit a flow towards the quantum chaotic regime.

• ### 24 February, 3pm UK time: Dr Hans Kessler (Universitat Hamburg)

Title: Dynamical phases in an atom cavity system

Abstract: We are experimentally exploring the lightmatter interaction of a Bose-Einstein condensate (BEC) with a single light mode of an ultra-high finesse optical cavity. The key feature of our cavity is the small field decay rate (𝜅/2𝜋 4.5 kHz), which is in the order of the recoil frequency (𝜔𝑟𝑒𝑐/2𝜋 3.56 kHz). This leads to a unique situation where cavity field evolves with the same timescale as the atomic distribution. If the system is pumped with a steady state light field, red detuned with respect to the atomic resonance, the Hepp-Lieb-Dicke phase transition of the open Dicke model is realized [1]. Starting in this self-ordered density wave phase and modulating the amplitude of the pump field, we observe a dissipative discrete time crystal, whose signature is a robust subharmonic oscillation between two symmetry-broken states [2]. On the other hand, modulation of a phase of the pump field can give rise to an incommensurate time crystal as proposed in [3]. For a blue-detuned pump light with respect to the atomic resonance, we propose an experimental realization of limit cycles. Since the model describing the system is time-independent (DC-driven), the emergence of a limit cycle phase heralds the breaking of continuous time-translation symmetry [4]. By periodically driving, the limit cycles stabilize and the system undergoes a transition from a continuous to a discrete time crystal [5].

[1] Klinder, J., Keßler, H., Wolke, M., Mathey, L., & Hemmerich, A. (2015). Dynamical phase transition in the open Dicke model. PNAS 112 (11), 3290-3295
[2] Keßler, H., Kongkhambut, P., Georges, C., Mathey, L., Cosme, J. G., & Hemmerich, A. (2020). Observation of a dissipative time crystal. arXiv preprint arXiv:2012.08885.
[3] Cosme, J. G., Skulte, J., & Mathey, L. (2019). Time crystals in a shaken atom-cavity system. Physical Review A, 100(5), 053615.
[4] Keßler, H., Cosme, J. G., Hemmerling, M., Mathey, L., & Hemmerich, A. (2019). Emergent limit cycles and time crystal dynamics in an atom-cavity system. Physical Review A, 99(5), 053605.
[5] Keßler, H., Cosme, J. G., Georges, C., Mathey, L., & Hemmerich, A. (2020). From a continuous to a discrete time crystal in a dissipative atom-cavity system. New Journal of Physics, 22(8), 085002.

• ### 3 March, 3pm UK time: Dr Mark Rudner (Niels Bohr Institute)

Title: Double feature: ‘Prethermal quantum pumps’ and ‘The universal Lindblad equation for many-body systems’

Abstract: In the quest to control the non-equilibrium dynamics of quantum many-body systems, we are faced with many challenges of both theoretical and experimental nature. Importantly, when isolated many-body systems are subjected to time-periodic driving fields, they tend to absorb energy and heat towards featureless states of maximal entropy density. However, nontrivial behavior may still be realized transiently, or in the steady states formed when coupling to a heat bath provides a balancing channel for energy dissipation. In the first part of this talk I will discuss a novel regime of prethermal dynamics in which the heating that naturally results from driving an isolated many-body system gives rise to quasisteady states displaying universal transport characteristics that reflect the topological features of the system’s underlying Floquet band structure. The quasisteady state features interesting oscillatory entanglement dynamics, and a striking robustness to disorder. In the second part of the talk I will describe a recently formulated Lindblad-form Markovian master equation, whose validity is justified independently of any restrictions on the energy level structure of the system. This “universal Lindblad equation” thus comprises an important new tool for studying open system dynamics in both static and driven systems.

• ### 10 March, 3pm UK: Dr Francesco Piazza (MPIPKS)

Controlling Cavity-Mediated Superconductivity with Quantum States of Light

Recently, it has become possible to couple electrons in two-dimensional materials to the quantum electromagnetic field of optical cavities. This realises a yet unexplored regime of Quantum Electrodynamics, which is non-relativistic, non-vacuum, and strongly coupled. Among many exciting avenues, one promising idea is to use the photons in the cavity to mediate pairing between electrons, inducing superconducting states with novel properties [1,2]. An exciting prospect, that makes photons the more interesting mediator with respect to the phonons of the standard BCS paradigm, is to exploit state-of-the-art engineering of the quantum states of light to control superconductivity. A naturally emerging question, which remains still open, is whether one can enhance superconductivity by feeding the cavity with certain quantum states of the photons. We recently developed a non-equilibrium field-theory approach that allows to tackle this question [3]. In this talk, I will describe our current understanding of the problem and first steps in answering the above.

[1] F. Schlawin, A. Cavalleri, and D. Jaksch, Phys. Rev. Lett. 122, 133602 (2019) [2] H. Gao, F. Schlawin, M. Buzzi, A. Cavalleri, and D. Jaksch, Phys. Rev. Lett. 125, 053602 (2020) [3] Ahana Chakraborty and Francesco Piazza, arXiv:2008.06513

• ### 17 March, 3pm UK time: Dr John Goold  (Trinity College Dublin)

Title: Quantum transport and eigenstate thermalisation

Abstract: How irreversible thermodynamics emerges from the unitary dynamics of the Schrödinger equation is a question that has been asked since the
inception of quantum theory itself. One modern take on the issue is the Eigenstate Thermalisation Hypothesis. In this talk I will discuss
the Eigenstate thermalisation hypothesis with special emphasis on the connection between off diagonal matrix elements of local observables and quantum transport. I will then give an overview and discussion of results from some recent works coming from the TCD group on the topic – in particular exploring integrability breaking with a local perturbation.

Relevant references:
‘’High temperature coherent transport in the XXZ chain in the presence of an
impurity”, M. Brenes, E. Mascarenhas, M. Rigol, J. Goold, PRB 98 235128 (2018)
“ Eigenstate Thermalisation Hypothesis in a locally perturbed integrable
system”, M. Brenes, T. LeBlond, J. Goold, M. Rigol, PRL 125 070605 (2020)
“Low frequency behaviour of off-diagonal matrix elements in the integrable
xxz chain and in a locally perturbed quantum chaotic chain”, M. Brenes, J. Goold, M. Rigol
PRB 102, 075127 (2020)
Out of time order correlations and fine structure of eigenstate thermalisation
M.Brenes et al, arXiv:2103.01161 (2021)https://www.youtube.com/watch?v=CvATAzbIxBw&ab_channel=LeedsLoughboroughNottinghamNonEqulibriumSeminar

• ### 14 April, 3pm UK time: Dr Graham Kells  ( Dublin Institute for Advanced Studies)

Using operator quantisation to explore topology at high-temperatures and in nonequilibrium
In this talk I will discuss the notion of operator – or third – quantisation. I will start by giving a visual tour of how and why it works and then review a few of the better known applications. I relation to our own work I will explain how it naturally leads to the notion of generalised modes and how we have used it to study the concept of strong zero-modes and what is called localisation enhanced topological order. I will finish by outlining how the method can be applied to an interesting model of quantum-classical transport – the transverse XY modified TASEP (Totally Asymmetric Simple Exclusion Process).

• ### 21 April, 3pm UK time: Dr Jad C. Halimeh, INO-CNR BEC Center and Department of Physics, University of Trento

Staircase Prethermalization and Constrained Dynamics in Lattice Gauge Theories

Abstract: The dynamics of lattice gauge theories is characterized by an abundance of local symmetry constraints. Although errors that break gauge symmetry appear naturally in NISQ-era quantum simulators, their influence on the gauge-theory dynamics is insufficiently investigated. In this talk, we show that a small gauge breaking of strength $\lambda$ induces a staircase of long-lived prethermal plateaus. The number of prethermal plateaus increases with the number of matter fields $L$, with the last plateau being reached at a timescale $\lambda^{−L/2}$, showing an intimate relation of the concomitant slowing down of dynamics with the number of local gauge constraints. By means of a Magnus expansion, we demonstrate how exact resonances between different gauge-invariant supersectors are the main reason behind the emergence of staircase prethermalization. Our results bode well for NISQ quantum devices, as they indicate that the proliferation timescale of gauge-invariance violation is counterintuitively delayed exponentially in system size. From a phenomenological perspective, our work shows how prethermal behavior is significantly enriched in models with slight breaking of local gauge invariance relative to their counterparts where a global symmetry is broken.

• ### 28 April, 3pm UK time: Dr Andrea Pizzi (Cambridge)

(Classical) Prethermal phases of matter in dimension 1, 2, and 3

Systems subject to a high-frequency drive can spend an exponentially long time in a prethermal regime, in which novel phases of matter with no equilibrium counterpart can be realized. Recent numerical investigations in this direction have been severely limited by the notorious computational challenges of many-body quantum mechanics. We show that prethermal non-equilibrium phases of matter also exist in classical Hamiltonian dynamics. First, we show that the phenomenology of known 1D quantum prethermal phases of matter is virtually the same when going classical, which suggests that these phenomena should in essence be thought of as robust to quantum fluctuations, rather than dependent on them. Second, we study the interplay between dimensionality and interaction range. For instance, we provide the first numerical proof of prethermal phases of matter in a system with short-range interactions, that are only possible in dimensionality 2 or 3. Concretely, we find higher-order as well as fractional discrete time crystals breaking the time-translational symmetry of the drive with unexpectedly large integer as well as fractional periods. Our work paves the way towards the exploration of novel prethermal phenomena by means of classical Hamiltonian dynamics with virtually no limitations on size nor dimensionality and with direct implications for experiments.

• ### 12 May, 3pm UK time: Dr Masud Haque (Maynooth)

Eigenstate Thermalization, random matrices and (non)local operators in many-body systems

The eigenstate thermalization hypothesis (ETH) is a cornerstone in our understanding of quantum statistical mechanics. The extent to which ETH holds for nonlocal operators (observables) is an open question.  I will address this question using an analogy with random matrix theory. The starting point will be the construction of extremely non-local operators, which we call Behemoth operators.  The Behemoths turn out to be building blocks for all physical operators.  This construction allow us to derive scalings for both local operators and different kinds of nonlocal operators.

• ### 19 May, 3pm UK time: Benjamin Doyon (KCL)

Operator ergodicity and hydrodynamic projection in many-body quantum systems
Obtaining rigorous results about the quantum dynamics of extended many-body systems is a difficult task. In quantum lattice models, the Lieb-Robinson bound tells us that the spatial extent of operators grows at most linearly in time. But what happens within this light-cone? I will discuss new rigorous results in this direction: a universal form of “operator ergodicity” showing that operators get “thinner” almost everywhere within the light-cone, which leads to a universal hydrodynamic projection formula for the large-time behaviour of correlation functions. The results are general, applicable to any locally interacting system, at arbitrary frequency and wavelength. Work in collaboration with Dimitrios Ampelogiannis.

• ### 02/06, 3pm UK time: Jens Bardarson (KTH)

Title: Time-evolution of local information—thermalization dynamics of local observables

Abstract: I discuss a way of organizing the flow of local information on a information lattice, consisting of the physical lattice supplemented by an extra dimension characterizing the scale of the information. Using this information lattice we observe different type of dynamics depending on the presence or absence of a finite thermalization time. This can then be used to construct algorithms for the time evolution of local information sufficient to calculate the expectation values of local observables. While this works in principle in any dimension we focus on simple modes in one dimension as a proof of principle.

https://www.youtube.com/watch?v=y7i-Ycv3ULw

# ****PLEASE NOTE THIS SEMINAR HAS BEEN POSTPONED FOR A LATER TIME****

Signatures of Chaos in Non-integrable Models of Quantum Field Theory

Despite the growing interest in the study of quantum chaos in many-body systems, numerical tests of chaoticity signatures, like spectral statistics, are almost exclusively limited to lattice models, leaving continuous models largely unexplored. Among them relativistic Quantum Field Theories (QFTs) and their dynamics lie at the cornerstone of important open questions of theoretical physics, like the black hole information paradox, making the study of ergodicity in QFT a topic of fundamental interest. Here we study signatures of quantum chaos in (1+1)D QFTs and show that, even though their level spacing statistics agree with the predictions of Random Matrix Theory, on the contrary, their eigenvector components follow a distribution markedly different from the expected Gaussian, raising questions on the validity of the Eigenstate Thermalisation Hypothesis in these models. To derive and validate our results we push the limits of the numerical method of Hamiltonian truncation beyond earlier studies and devise strict measures of the truncation error.

• ### 16/06, 3pm UK time: Dr Alessio Lerose (Geneva)

Influence matrix approach to quantum many-body dynamics

A basic and ubiquitous phenomenon in nonequilibrium dynamics of isolated quantum many-body systems is local thermalization. This is commonly described as the ability of a system to act as an effective thermal bath for its local subsystems, and usually probed via global spectral characteristics. Understanding the microscopic mechanism of quantum thermalization, and above all of its failures, is currently the subject of intensive theoretical and experimental investigations. In this talk, I will introduce an approach to study quantum many-body dynamics, inspired by the Feynman-Vernon influence functional theory of quantum baths. Its central object is the influence matrix (IM), which describes the effect of a Floquet many-body system on the evolution of its local subsystems. For translationally invariant one-dimensional systems, the IM obeys a self-consistency equation. For certain fine-tuned models, remarkably simple exact solutions appear, which physically represent perfect dephasers (PD), i.e., many-body systems acting as perfectly Markovian baths on their parts. Such PDs include certain solvable quantum circuits discovered and investigated in recent works. In the vicinity of PD points, the system is not perfectly Markovian, but rather acts as a quantum bath with a short memory time. In this case, we demonstrate that the self-consistency equation can be solved using matrix-product states (MPS) methods, as the IM temporal entanglement is low. The underlying “principle of efficiency” of quantum dynamics simulations is complementary to that of standard methods, as it only relies on short-range temporal correlations. Using a combination of analytical insights and MPS computations, we characterize the structure of the IM in terms of an effective “statistical-mechanics” description for local quantum trajectories and illustrate its predictive power by analytically computing the relaxation rate of an impurity embedded in the system.
In the last part of the talk, I will describe how to extend these ideas to study the many-body localized (MBL) phase of strongly disordered periodically kicked interacting spin chains. This approach allows to study exact disorder-averaged time evolution in the thermodynamic limit. MBL systems fail to act as efficient baths, and this property is encoded in their IM. I will discuss the structure of an MBL IM and link it to the onset of temporal long-range order.

References:

[1] Influence matrix approach to many-body Floquet dynamics arXiv:2009.10105 (2020) Phys. Rev. X 11, 021040
[2] Characterizing many-body localization via exact disorder-averaged quantum noise arXiv:2012.00777 (2020)
[3] Influence functional of many-body systems: temporal entanglement and matrix-product state representation arXiv:2103.13741 (2021) (to appear in Annals of Physics)
[4] Scaling of temporal entanglement in proximity to integrability arXiv:2104.07607 (2021)

• ### 23/06, 3pm UK time: Fabien Alet (Toulouse)

Probing for many-body localization in two dimensional disordered constrained systems

Many-body localization is a unique physical phenomenon driven by interactions and disorder for which a quantum system can evade thermalization. While the existence of a many-body localized phase is now well established in one-dimensional systems, its fate in higher dimension is an open question. In this talk, I will present a numerical study of the possibility of many-body localization transition in disordered quantum dimer models on the square and honeycomb lattices. I will present a critical review of our numerical results using state-of-the-art exact diagonalization and time evolution methods, probing both eigenstates and dynamical properties. We conclude for the existence of a localization transition, on the available time and length scales (up to N=108 sites on the honeycomb lattice).

Work done in collaboration with H. Théveniaut. G. Meyer, Z. Lan and F. Pietracaprina.

• ### 22 September, 3pm UK time: Ivan Khaymovich (MPI-PKS Dresden)

Title: Random-matrix approach to slow dynamics in quantum systems
Abstract:
In this talk, we will discuss a random-matrix approach to the description of disordered many-body systems and their Hilbert-space structure, focusing on ergodicity breaking effects and slow dynamics in such models. As a generic example of this approach, we consider the static and the dynamical phases in a Rosenzweig-Porter random matrix ensemble with a distribution of off-diagonal matrix elements of the form of the large-deviation ansatz.  We present a general theory of survival probability in such a random-matrix model and show that the averaged survival probability may decay with time as a simple exponent, as a stretch-exponent and as a power-law or slower. Correspondingly, we identify the exponential, the stretch-exponential and the frozen-dynamics phases.  We consider the mapping of the Anderson localization model on Random Regular Graph, the known proxy of MBL, onto the RP model and find exact values of the stretch-exponent kappa in the thermodynamic limit.  Our theory allows to describe analytically the finite-size multifractality and to compute the critical length with the exponent 1 associated with it.
Corresponding publication:
I. M. Khaymovich and V. E. Kravtsov “Dynamical phases in a “multifractal” Rosenzweig-Porter model” SciPost Physics 11, 045 (2021).