Mean Field Theory of the Localization Transition

TL;DR

This paper develops a mean field theory to understand the localization transition in bosonic systems, revealing the role of energy distribution and identifying a new Bose-glass phase through various calculated physical quantities.

Contribution

It introduces a mean field framework for localization in bosonic systems and characterizes the Bose-glass phase based on energy distribution effects.

Findings

Localization depends on the distribution of site energies.

A Bose-glass phase is identified with specific physical signatures.

Critical exponents for various quantities are determined.

Abstract

A mean field theory of the localization transition for bosonic systems is developed. Localization is shown to be sensitive to the distribution of the random site energies. It occurs in the presence of a triangular distribution, but not a uniform one. The inverse participation ratio, the single site Green's function, the superfluid order parameter and the corresponding susceptibility are calculated, and the appropriate exponents determined. All of these quantities indicate the presence of a new phase, which can be identified as the {\it Bose-glass}.