Deformation of localized states and state transitions in systems of randomly hopping interacting fermions

TL;DR

This paper investigates how interactions affect localized states in a disordered fermionic system, revealing localization resurgence in the ground state and extension in excited states, using numerical and analytical methods.

Contribution

It demonstrates how repulsive interactions deform localized eigenstates and introduces a solvable model to understand the transition of local integrals of motion.

Findings

Localization resurgence in the ground state due to repulsion

Excited states tend to become extended with interactions

Explicit construction of LIOMs in the solvable model

Abstract

We numerically study the random-hopping fermions (the Cruetz ladder) with repulsion and investigate how the interactions deform localized eigenstates by means of the one particle-density matrix (OPDM). The ground state exhibits resurgence of localization from the compact localized state to strong-repulsion-induced localization. On the other hand, excited states in the middle of the spectrum tend to extend by the repulsion. The transition property obtained by numerical calculations of the OPDM is deeply understood by studying a solvable model in which local integrals of motion (LIOMs) are obtained explicitly. The present work clarifies the utility of the OPDM and also how compact-support LIOMs in non-interacting limit are deformed by the repulsion.