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

arXiv eprints
 Pub Date:
 March 2023
 DOI:
 10.48550/arXiv.2303.11148
 arXiv:
 arXiv:2303.11148
 Bibcode:
 2023arXiv230311148R
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 17 pages, 5 figures