Many-body localization of spinless fermions with attractive interactions in one dimension

TL;DR

This paper investigates the phase diagram of one-dimensional spinless fermions with attractive interactions, revealing that the zero-temperature Luttinger liquid phase extends into finite-energy densities, evolving smoothly into an ergodic phase without intermediate transitions.

Contribution

It demonstrates that the finite-energy density phase diagram features a smooth transition from the Luttinger liquid to an ergodic phase, using novel measures and computational methods.

Findings

Luttinger liquid persists at finite energy densities.

Occupation-spectrum discontinuity is smaller in Luttinger liquids.

No intermediate phase transition between Luttinger liquid and ergodic phase.

Abstract

We study the finite-energy density phase diagram of spinless fermions with attractive interactions in one dimension in the presence of uncorrelated diagonal disorder. Unlike the case of repulsive interactions, a delocalized Luttinger-liquid phase persists at weak disorder in the ground state, which is a well-known result. We revisit the ground-state phase diagram and show that the recently introduced occupation-spectrum discontinuity computed from the eigenspectrum of one-particle density matrices is noticeably smaller in the Luttinger liquid compared to the localized regions. Moreover, we use the functional renormalization scheme to study the finite-size dependence of the conductance, which resolves the existence of the Luttinger liquid as well and is computationally cheap. Our main results concern the finite-energy density case. Using exact diagonalization and by computing various established measures of the many-body localization-delocalization transition, we argue that the zero-temperature Luttinger liquid smoothly evolves into a finite-energy density ergodic phase without any intermediate phase transition.