Quantum Coulomb gap in low dimensions

We study the single-particle density of states of one- and two-dimensional quantum disordered systems in the strongly localized regime with long-range interactions. We consider a 1/root 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 use an exact diagonalization technique for small system sizes and a perturbation approach for larger sizes. 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.