Buca, Berislav

Date:    Tuesday April 18, 2023
Time:    11:00am
Place:   ETH Campus Hönggerberg, HPF G6
Host:    Tobias Donner 

Eigenoperator thermalization theory 

Berislav Buca, Niels Bohr Institute, University of Copenhagen and Department of Physics, University of Oxford

Abstract: I will provide a rigorous 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).