Universal properties of single particle excitations across the many-body localization transition

TL;DR

This paper investigates the universal properties of single-particle excitations across the many-body localization transition in disordered one-dimensional fermionic systems, revealing a continuous transition and critical exponents consistent with theoretical bounds.

Contribution

It introduces a finite size scaling analysis of local density of states and scattering rates, providing new insights into the nature of the MBL transition and critical exponents.

Findings

The MBL transition is continuous in one-dimensional models.

Critical exponents satisfy the CCFS bound when analyzing local density of states.

Level-spacing ratio diagnostics violate the CCFS bound, unlike single-particle observables.

Abstract

Understanding the nature of the transition from the delocalized to the many-body localized (MBL) phase is an important unresolved issue. To probe the nature of the MBL transition, we investigate the universal properties of single-particle excitations produced in highly excited many-body eigenstates of a disordered interacting quantum many-body system. In a class of one-dimensional spinless fermionic models with random disorder, we study the finite size scaling of the ratio of typical to average values of the single-particle local density of states and the scattering rates across the MBL transition. Our results indicate that the MBL transition in this class of one-dimensional models of spinless fermions is continuous in nature. For various ranges of interactions in the system, the critical exponent $\nu$ with which the correlation length $\xi$ diverges at the transition point $W_c$, $\xi \sim |W-W_c|^{-\nu}$, satisfies the Chayes-Chayes-Fisher-Spencer(CCFS) bound $\nu \ge 2/d$ where $d$ is the physical dimension of the system. We also discuss why the critical exponent obtained from finite-size scaling of the conventional diagnostic of many-body localization, the level-spacing ratio, strongly violates the CCFS bound while the single-particle density of states and scattering rates are consistent with the CCFS criterion.