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Leeds-Loughborough-Nottingham Seminars Archive 2022/23

Past seminars in 2022/23

  • 17/05/2022, 3pm: Alvaro M. Alhambra (Autonomous University of Madrid)

Title: Classical simulation of short-time quantum dynamics
Abstract: Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this problem in order to benchmark quantum simulators and to delineate the regime of quantum advantage. Here we present classical algorithms for approximating the dynamics of local observables and nonlocal quantities such as the Loschmidt echo, where the evolution is governed by a local Hamiltonian. For short times, their computational cost scales polynomially with the system size and the inverse of the approximation error. In the case of local observables, the proposed algorithm has a better dependence on the approximation error than algorithms based on the Lieb–Robinson bound. Our results use cluster expansion techniques adapted to the dynamical setting, for which we give a novel proof of their convergence. This has important physical consequences besides our efficient algorithms. In particular, we establish a novel quantum speed limit, a bound on dynamical phase transitions, and a concentration bound for product states evolved for short times.
Joint work with Dominik S. Wild (arXiv:2210.11490)

Previous seminars

  • 15 March, 3pm: Berislav Buca (Niels Bohr Institute, University of Copenhagen and Department of Physics, University of Oxford)

Title: Eigenoperator thermalization theory
Abstract: I will provide a rigorous operator algebraic framework of dynamics in locally interacting systems in any dimension. It is based on pseudolocal dynamical symmetries generalising pseudolocal charges. This generalization proves sufficient to construct a theory of all sufficiently local quantum many-body dynamics in closed, open and time-dependent systems, in terms of time-dependent generalized Gibbs ensembles. These ensembles unify seemingly disparate manifestations of quantum non-ergodic dynamics including quantum many-body scars, continuous, discrete and dissipative time crystals, Hilbert space fragmentation, lattice gauge theories, and disorder-free localization. In the process novel pseudo-local classes of operators are introduced: "restricted local", which are local only for some states, and "crypto-local", whose locality is not manifest in terms of any finite number of local densities. This proven theory is intuitively the rigorous algebraic counterpart of the eigenstate thermalization hypothesis and has implications for thermodynamics: quantum many-body systems, rather than merely reaching a Gibbs ensemble in the long-time limit, are always in a time-dependent generalized Gibbs ensemble for any natural initial state.

References:

Berislav Buca. Unified theory of local quantum many-body dynamics: Eigenoperator thermalization theorems. arXiv:2301.07091 (2023).

Benjamin Doyon. Thermalization and pseudolocality in extended quantum systems. Commun. Math. Phys. 351: 155-200 (2017).

  • 22 February, 3pm: Matteo Ippoliti (Stanford)

Title: Optimizing classical shadows with insights from quantum dynamicsAbstract: Classical shadows are a powerful method for learning many properties of quantum states from relatively few measurements. The method is based on randomized measurements, and its performance on different tasks depends crucially on the choice of randomizing (or "twirling") procedure. I will give an overview of the method in a physics-oriented language, and present recent work [1] in which we relate the performance of classical shadows to fundamental properties of operator evolution under chaotic dynamics. In particular, we analyze the problem of learning expectation values of local Pauli operators, and find that its sample complexity (i.e. the number of experiments needed) is dictated by the competition of two processes under random-circuit dynamics: the expansion of an operator's support (operator spreading), and the equilibration of local Pauli density inside the support ("operator relaxation"). Based on this insight, we identify the optimal circuit depth for the twirling circuit and the associated sample complexity. Our work sheds light on the inner workings of classical shadows, and makes contact between fundamental ideas in nonequilibrium quantum physics and applications to quantum information science.[1] MI, Y. Li, T. Rakovzsky and V. Khemani, arXiv:2212.11963

  • 21 February, 3pm: Lenart Zadnik (SISSA)

Title: The folded XXZ modelAbstract: The large-anisotropy limit of the anisotropic Heisenberg spin-1/2 chain gives rise to the so-called folded XXZ model. This talk will mainly be a summary of what is and what is not yet known about this kinetically constrained model, and of a rich palette of phenomena that emerge in it. I will provide a brief explanation of the folded model’s origin, of its symmetries, of the quasiparticle content constituting its Bethe Ansatz solution, and of its aspects that are still not understood. I will explain how the symmetries emergent in the large anisotropy limit of the Heisenberg model result in a rich Hilbert space structure, exhibiting strong fragmentation and a Fibonacci sector of jammed states. A particular feature of the jammed states, which I will mention, is a somewhat counterintuitive dynamical phenomenon, in which a localised perturbation can have everlasting macroscopic effects.

  • 15 February, 3pm: Kiryl Pakrouski (ETH Zurich)

Title: Weak ergodicity breaking in fermionic lattice models

Abstract: Many-body scars are states that do not obey the eigenstate thermalization hypothesis and thus lead to weak ergodicity breaking. Time evolution starting from a mix of such states exhibits "revivals" - the system returns to the exact initial state after equal periods of time. We will first introduce a general recipe for constructing Hamiltonians with scars inspired by the group theory. Such Hamiltonians have the form H0+O*T, where T is a generator of an appropriate Lie group. We will then specialise this to the case of spin-1/2 fermions on a lattice. Here we show that three families of highly symmetric states are many-body scars. One of these families consists of the well-known eta-pairing states discussed by Yang in the context of superconductivity. All of these states have potential advantages for storing and processing quantum information. We show that it is natural to choose T to be hopping on a lattice. With this choice a number of well-known coupling terms, such as the Hubbard and the Heisenberg interactions, and the Hamiltonians containing them (including topological ones), decompose in the required form and support the three families of states as scars without fine-tuning. We also discuss the conditions for the low-energy subspace of these models to be comprised solely of scars. We expand the framework to the non-Hermitian (open) systems and demonstrate that for them the scar subspace continues to undergo coherent time evolution and exhibit "revivals". Finally, we discuss the generalization of this approach to multi-band models.

Based on
arXiv:2007.00845
arXiv:2106.10300
arXiv:2212.11914

 

  • 18 January, 3pm: Zohar Nussinov, Washington University St Louis

 

  • 7 December, 3pm: Lorenzo Piroli, ENS

  • 29 November, 3pm: Gil Refael, Caltech

  • 23 November, 3pm: Curt von Keyserlingk, Kings College London

  • 16 November, 3pm: Žiga Krajnik, Ljubljana

  • 2 November, 3pm: Maarten van Damme, Ghent

Title: Tangent vectors and spectral functions
Abstract: Spectral functions are perhaps the most elementary dynamical quantity. They are not only interesting by themselves, as a clear signature of the low-lying excitations, but they are also experimentally measurable. This makes them an important target for numerical simulations. In this talk I will go over some recent algorithmic developments in the field of tensor networks that are relevant for non-equilibrium physics, primarily focused on the calculation of spectral functions.

  • 26 October, 3pm: Max McGinley, Oxford

Title: Measuring many properties of a quantum state in analog quantum simulators

Abstract: One of the many potential uses of a quantum computer is to simulate complex many-body quantum phenomena that would be computationally intractable on a classical computer. At present, fully programmable quantum computers are limited in terms of their size and noisiness. However, some experimental platforms are particularly well-suited to quantum simulation, even if they do not possess full programmability. In such analog quantum simulators, which include ultracold atomic gases and arrays of Rydberg atoms in optical tweezers, one typically has global control over interactions, instead of individual site-selective control. While this allows many interesting kinds of dynamics to be synthesised, accessing expectation values of certain observables remains challenging, due to the intrinsic limitations in programmability. In this talk, I will introduce a scheme that allows one to measure any property of a quantum state, including nonlinear functionals such as Renyi entropies, using only global control over the dynamics, making it particularly well-suited to analog quantum simulators. Crucially, the total number of experimental repetitions required to estimate a collection of observables can be bounded in the same way as in classical shadow tomography [1], which is a provably optimal protocol designed for fully programmable devices. The success of our scheme is rooted in the recently discovered phenomenon of "deep thermalization" [2], where quantum state designs emerge naturally from deterministic chaotic dynamics. I will present simulations of our protocol, which allow us to benchmark its performance, and discuss how the effects of noise can be mitigated. [1] Huang et al., Nat. Phys. 16, 1050 (2020) [2] Cotloer et al., arXiv:2103.03536 This talk is based on: MM, M. Fava, S. Biswas (arXiv -- to appear)

  • 05/10/2022, 3pm: Jonathon Riddell (McMaster University)Title: Concentration of equilibration and an estimate of the recurrence timeAbstract: In this talk we will first explore the problem of equilibration and the emergence of static equilibrium in isolated quantum many body systems. We will then show that the dynamics of generic quantum systems concentrate around their equilibrium value when measuring at arbitrary times. In particular, we show that the probability of finding the system away from equilibrium is doubly exponentially supressed in system size. We will then use these concentration results to put a lower bound on the recurrence time.