A Floquet Model for the Many-Body Localization Transition

TL;DR

This paper introduces a Floquet spin chain model to study the many-body localization transition, demonstrating that it effectively captures the transition behavior even at small sizes and avoids complications from conservation laws.

Contribution

The authors propose a Floquet model with no local conservation laws that enhances the detection of the MBL transition in finite-size systems.

Findings

Standard diagnostics behave well in the Floquet model.

The spacetime correlation function peaks at the transition.

Conservation laws affect correlation functions in Hamiltonian models.

Abstract

The nature of the dynamical quantum phase transition between the many-body localized (MBL) phase and the thermal phase remains an open question, and one line of attack on this problem is to explore this transition numerically in finite-size systems. To maximize the contrast between the MBL phase and the thermal phase in such finite-size systems, we argue one should choose a Floquet model with no local conservation laws and rapid thermalization to "infinite temperature" in the thermal phase. Here we introduce and explore such a Floquet spin chain model, and show that standard diagnostics of the MBL-to-thermal transition behave well in this model even at modest sizes. We also introduce a physically motivated spacetime correlation function which peaks at the transition in the Floquet model, but is strongly affected by conservation laws in Hamiltonian models.