Local density of states and scattering rates across the many-body localization transition

TL;DR

This paper investigates the many-body localization transition in disordered quantum systems by analyzing local density of states and scattering rates, revealing distinct signatures and distributions across phases.

Contribution

It provides the first detailed analysis of single-particle Green's functions and their distributions across the MBL transition in a disordered 1D system.

Findings

Finite typical local density of states in delocalized phase

Vanishing local density of states in MBL phase

Broad log-normal distributions in delocalized phase

Abstract

Characterizing the many-body localization (MBL) transition in strongly disordered and interacting quantum systems is an important issue in the field of condensed matter physics. We study the single particle Green's functions for a disordered interacting system in one dimension using exact diagnonalization in the infinite temperature limit and provide strong evidence that single particle excitations carry signatures of delocalization to MBL transition. In the delocalized phase, the typical values of the local density of states and the scattering rate are finite while in the MBL phase, the typical values for both the quantities become vanishingly small. The probability distribution functions of the local density of states and the scattering rate are broad log-normal distributions in the delocalized phase while the distributions become very narrow and sharply peaked close to zero in the MBL phase. We also study the eigenstate Green's function for all the many-body eigenstates and demonstrate that both, the energy resolved typical scattering rate and the typical local density of states, can track the many-body mobility edges.