Effect of disorder on the interacting Fermi gases in a one-dimensional optical lattice

TL;DR

This paper investigates how correlated disorder affects the phase structure and compressibility of interacting Fermi gases in a one-dimensional optical lattice, revealing disorder-induced destruction of insulating regions and anomalies in compressibility.

Contribution

It provides a theoretical analysis using density-functional theory to understand disorder effects on ground-state phases of 1D Fermi gases, including the impact on insulating regions and compressibility anomalies.

Findings

Disorder destroys local insulating regions when strong enough.

Disorder induces anomalies in inverse compressibility at low density.

Large disorder correlation length reduces compressibility enhancement.

Abstract

Interacting two-component Fermi gases loaded in a one-dimensional (1D) lattice and subjected to an harmonic trapping potential exhibit interesting compound phases in which fluid regions coexist with local Mott-insulator and/or band-insulator regions. Motivated by experiments on cold atoms inside disordered optical lattices, we present a theoretical study of the effects of a correlated random potential on these ground-state phases. We employ a lattice version of density-functional theory within the local-density approximation to determine the density distribution of fermions in these phases. The exchange-correlation potential is obtained from the Lieb-Wu exact solution of Fermi-Hubbard model. On-site disorder (with and without Gaussian correlations) and harmonic trap are treated as external potentials. We find that disorder has two main effects: (i) it destroys the local insulating regions if it is sufficiently strong compared with the on-site atom-atom repulsion, and (ii) it induces an anomaly in the inverse compressibility at low density from quenching of percolation. For sufficiently large disorder correlation length the enhancement in the inverse compressibility diminishes.