Quantum Coulomb gap in low dimensions

TL;DR

This paper investigates the density of states in low-dimensional quantum disordered systems with Coulomb interactions, revealing that finite hopping reduces but does not eliminate the linear Coulomb gap.

Contribution

It demonstrates that the linear Coulomb gap persists in low dimensions despite finite hopping, using both exact diagonalization and perturbation methods.

Findings

Linear gaps are present in 1D and 2D systems with Coulomb interactions.

Finite hopping reduces the slope of the Coulomb gap.

The linear character of the gap remains unchanged with finite hopping.

Abstract

We study the single-particle density of states of one-dimensional and two-dimensional quantum disordered systems with long-range interactions. We consider a $1/\sqrt{r}$ interaction in one dimension and a Coulomb interaction in two dimensions, which produce linear gaps in the density of states in both cases. We focus on the strong localization regime where the localization length is small but non-zero. We use an exact diagonalization technique for small system sizes and a perturbation approach for larger sizes. We find that, with both methods, the inclusion of a finite hopping contribution does not change the linear character of the gap, but reduces its slope, widening the gap.