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DY: Fachverband Dynamik und Statistische Physik

DY 17: Many-body Systems: Equilibration, Chaos, and Localization (joint session DY/TT)

DY 17.1: Talk

Tuesday, March 19, 2024, 09:30–09:45, A 151

Non-equilibration, synchronization, and time crystals in isotropic Heisenberg models — •Jürgen Schnack, Patrick Vorndamme, and Peter Reimann — Bielefeld University

Isotropic, but otherwise largely arbitrary Heisenberg models in the presence of a homogeneous magnetic field are considered, including various integrable, non-integrable, as well as disordered examples, and not necessarily restricted to one dimension or short-range interactions. Taking for granted that the non-equilibrium initial condition and the spectrum of the field-free model satisfy some very weak requirements, expectation values of generic observables are analytically shown to exhibit permanent long-time oscillations, thus ruling out equilibration [1]. If the model (but not necessarily the initial condition) is translationally invariant, the long-time oscillations are moreover shown to exhibit synchronization in the long run, meaning that they are invariant under arbitrary translations of the observable [2]. Analogous long-time oscillations are also recovered for temporal correlation functions when the system is already at thermal equilibrium from the outset, thus realizing a so-called time crystal.

[1] P. Reimann, P. Vorndamme, J. Schnack, Phys. Rev. Research 5, 043040 (2023)

[2] P. Vorndamme, H.-J. Schmidt, Chr. Schröder, J. Schnack, New J. Phys. 23, 083038 (2021)

Keywords: Equilibration; quantum spin system; SU(2) symmetry; unitary time evolution; synchronization