Local integrals of motion and the quasiperiodic many-body localization transition

TL;DR

This paper investigates the many-body localization transition in quasiperiodic systems by analyzing local integrals of motion, revealing a discontinuous change at the transition and suggesting a different critical behavior than previously thought.

Contribution

It introduces a numerical method to study LIOMs across the MBL transition and finds a sharper, discontinuous change indicating a potentially different universality class.

Findings

Norm of time-averaged operators drops discontinuously at transition

LIOMs become unstable at a critical localization length

Transition occurs at stronger modulations with larger critical exponent

Abstract

We study the many body localization (MBL) transition for interacting fermions subject to quasiperiodic potentials by constructing the local integrals of motion (LIOMs) in the MBL phase as time-averaged local operators. We study numerically how these time-averaged operators evolve across the MBL transition. We find that the norm of such time-averaged operators drops discontinuously to zero across the transition; as we discuss, this implies that LIOMs abruptly become unstable at some critical localization length of order unity. We analyze the LIOMs using hydrodynamic projections and isolating the part of the operator that is associated with interactions. Equipped with this data we perform a finite-size scaling analysis of the quasiperiodic MBL transition. Our results suggest that the quasiperiodic MBL transition occurs at considerably stronger quasiperiodic modulations, and has a larger correlation-length critical exponent, than previous studies had found.