Exact results for one-dimensional disordered bosons with strong repulsion

TL;DR

This paper analyzes one-dimensional disordered bosons with strong repulsion, using a Bose-Fermi mapping to derive exact results for their spectral and correlation properties, with implications for ultracold atomic gas experiments.

Contribution

It provides exact analytical results for disordered strongly interacting bosons in one dimension by mapping to free fermions, extending known results to disordered systems.

Findings

Density-density correlations are characterized.

Distribution function of local density of states is obtained.

Spectral statistics are fully described.

Abstract

We study one-dimensional incommensurate bosons with strong repulsive interactions and weak disorder. In analogy to the clean Tonks-Girardeau gas, a Bose-Fermi mapping expresses this problem in terms of disordered free fermions. Thereby many known results apply, in particular for the density-density correlations, the distribution function of the local density of states, and the complete spectral statistics. We also analyze the bosonic momentum distribution, and comment on the experimental observability of these predictions in ultracold atomic gases.