Simulation of many body localization and time crystals in two dimensions with the neighborhood tensor update

TL;DR

This study uses the neighborhood tensor update algorithm to simulate many-body localization and time crystal phenomena in a two-dimensional disordered Heisenberg model, revealing long-lived localized and time crystalline phases.

Contribution

First application of NTU algorithm to 2D disordered Heisenberg model demonstrating many-body localization and Floquet time crystal phases.

Findings

Identification of many-body localized regime at strong disorder

Observation of Floquet time crystalline behavior under periodic driving

Long evolution times achieved with bond dimension up to 20

Abstract

The Heisenberg antiferromagnet with discrete disorder on an infinite square lattice is evolved in time from an initial N\'eel state. The simulation is performed with the neighborhood tensor update (NTU) algorithm for an infinite projected entangled pair state (iPEPS) [Phys. Rev. B 104, 094411 (2021)]. Ancillary spins are used to average over $2$ or $5$ discrete values of disorder. With a bond dimension up to $20$, evolution times are long enough to identify a many body localized regime for a strong enough disorder. Furthermore, the same Hamiltonian is subject to periodic spin flips. Simulations of the Floquet dynamics show that it can sustain a time crystalline stage for a strong enough disorder.