Many-body ground state localization and coexistence of localized and extended states in an interacting quasiperiodic system

TL;DR

This paper investigates the transition from extended to many-body localized phases in an interacting quasiperiodic system, revealing an intermediate coexistence phase characterized by both localized and extended states.

Contribution

It identifies an intermediate phase with coexisting localized and extended many-body states in an interacting quasiperiodic system, distinct from the noninteracting case.

Findings

Existence of an intermediate phase with coexisting states

Characterization of phases using participation ratios and natural orbital distributions

Difference from noninteracting localization transition

Abstract

We study the localization problem of one-dimensional interacting spinless fermions in an incommensurate optical lattice, which changes from an extended phase to a nonergoic many-body localized phase by increasing the strength of the incommensurate potential. We identify that there exists an intermediate regime before the system enters the many-body localized phase, in which both the localized and extended many-body states coexist, thus the system is divided into three different phases, which can be characterized by normalized participation ratios of the many-body eigenstates and distributions of natural orbitals of the corresponding one-particle density matrix. This is very different from its noninterating limit, in which all eigenstaes undergo a delocaliztion-localization transtion when the strength of the incommensurate potential exceeds a critical value.