Following the tradition from the previous years,  the Universities of Leeds (Dr. Papic), Loughborough (Dr. Lazarides) and Nottingham (Dr. Bertini) will be running a joint hybrid seminar series on non-equilibrium physics during 2022/23. “Hybrid” means that some of the seminars will be delivered in person in one of the Universities and broadcast remotely in others, while some seminars will be fully online.

The seminars will be on Zoom and typically take place on Wednesdays at 3pm UK time:

Leeds-Loughborough-Nottingham Zoom Seminar

https://universityofleeds.zoom.us/j/81863636407?pwd=aitNN0pXWmJGSjhUMFFCVnFrSys1Zz09

Meeting ID: 818 6363 6407

Passcode: 1828#Ab

For a complete list of previous seminars in 2020/21 and 2021/22, please see the archive on the left.

Seminar schedule (evolving)

Previous seminars

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

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 dynamics

Abstract: 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)

• 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

• 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 time
  
  Abstract: 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.