Diagnostics of nonergodic extended states and many body localization proximity effect through real-space and Fock-space excitations

TL;DR

This paper investigates the properties of ergodic, nonergodic extended, and many-body localized phases in a quasiperiodic system, revealing how a mobility edge persists with interactions and how NEE and MBL states differ through real-space and Fock-space analyses.

Contribution

It introduces a combined real-space and Fock-space framework to distinguish NEE and MBL phases, highlighting the survival of the mobility edge and differences in Fock-space propagator decay.

Findings

Mobility edge persists in NEE phase with interactions.

All single-particle excitations localize in MBL phase due to proximity effect.

N-E and MBL states are similar in multifractality but differ in Fock-space propagator decay.

Abstract

We provide real-space and Fock-space (FS) characterizations of ergodic, nonergodic extended (NEE) and many-body localized (MBL) phases in an interacting quasiperiodic system, namely generalized Aubry-Andr\'e-Harper model, which possesses a mobility edge in the non-interacting limit. We show that a mobility edge in the single-particle (SP) excitations survives even in the presence of interaction in the NEE phase. In contrast, all SP excitations get localized in the MBL phase due to the MBL proximity effect. We give complementary insights into the distinction of the NEE states from the ergodic and MBL states by computing local FS self-energies and decay length associated, respectively, with the local and the non-local FS propagators. Based on a finite-size scaling analysis of the typical local self-energy across the NEE to ergodic transition, we show that MBL and NEE states exhibit qualitatively similar multifractal character. However, we find that the NEE and MBL states can be distinguished in terms of the decay of the non-local propagator in the FS, whereas the typical local FS self-energy cannot tell them apart.