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 the one-particle density matrix is noticeably smaller in the Luttinger liquid compared to the localized regions. Moreover, we use the functional renormalization group scheme to study the finite-size dependence of the conductance, which also resolves the existence of the Luttinger liquid 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.
Highlights
We further demonstrate that the zero-temperature disorder-interaction phase diagram can be obtained from a calculation of the conductance using the functional renormalization group method, with qualitative agreement with other methods
In this work we studied the finite energy-density phase diagram of spinless fermions in a onedimensional lattice with attractive interactions and uncorrelated disorder
Our numerical results illustrate an asymmetry between the V < 0 and V > 0 phase diagrams, rooted in the existence of a delocalized phase in the ground state of the system with attractive interactions and weak disorder [28, 29]
Summary
A much studied model for the interplay between disorder and interactions at finite energy densities are spinless fermions in a one-dimensional lattice with uncorrelated diagonal disorder and nearest-neighbor repulsive interactions. Similar to the case of repulsive interactions, we expect an ergodic phase at weak disorder. The latter scenario would imply an inverted mobility edge. This implies certain values for the average of the gap ratio in these two cases, namely [rgap] ≈ 0.3863 and [rgap] ≈ 0.5307, respectively (see the discussion in [1])
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