QLunch: Berislav Buca

Speaker: Berislav Buca (Niels Bohr Institute, University of Copenhagen and Department of Physics, University of Oxford)

Title: Eigenoperator thermalization theory

Abstract: Locality is an important physical principle, even in non-relativistic lattice models for which the Lieb-Robinson bound may be given, providing strong constraints on how fast signals can propagate. I will provide a rigorous operator algebraic framework of dynamics in locally interacting systems in any dimension. Crucial quantities are called "pseudolocal" and are defined via a Gelfand–Naimark–Segal (GNS) construction, intuitively embodying extensivity of the dynamics. This generalization proves sufficient to construct a theory of all local quantum many-body dynamics in closed, open and time-dependent systems, in terms of time-dependent generalized Gibbs ensembles.

More precisely, I will prove that the dynamics is given by a strongly continuous quantum semigroup and the state of local observables (in a weak- sense) is always an equilibrium ensemble, but with time dependent chemical potentials. 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 thermalizing to a Gibbs ensemble in the long-time limit, are actually always in a time-dependent generalized Gibbs ensemble for any natural initial state.

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).