Characterizing dynamical criticality of many-body localization transitions from the Fock-space perspective

TL;DR

This paper investigates many-body localization transitions using Fock-space dynamics, revealing different critical behaviors in models with random, quasiperiodic, and Floquet systems through finite-size scaling analysis.

Contribution

It introduces a Fock-space displacement approach to characterize MBLTs and compares continuous and BKT scaling, providing new insights into the nature of these transitions.

Findings

Random field and Floquet models share similar scaling exponents.

Quasiperiodic model exhibits different critical behavior.

BKT scaling better describes certain MBLTs, indicating larger critical points.

Abstract

Characterizing the nature of many-body localization transitions (MBLTs) and their potential critical behaviors has remained a challenging problem. In this work, we study the dynamics of the displacement, quantifying the spread of the radial probability distribution in the Fock space, for three systems with MBLTs, i.e., the Hamiltonian models with quasiperiodic and random fields, as well as a random-circuit Floquet model of a MBLT. We then perform a finite-size scaling analysis of the long-time averaged displacement by considering two types of ansatz for MBLTs, i.e., continuous and BKT transitions. The data collapse based on the assumption of a continuous phase transition with power-law correlation length reveals that the scaling exponent of the MBLT induced by random field is close to that of the Floquet model, but significantly differes from the quasiperiodic model. Additionally, we find that the BKT-type scaling provides a more accurate description of the MBLTs in the random model and the Floquet model, yielding larger (finite-size) critical points compared to those obtained from power-law scaling. Our work highlights that the displacement is a valuable tool for studying MBLTs, as relevant to ongoing experimental efforts.