Superfluid - Bose glass transition in two dimensions at T = 0: analytic solution of a mode-coupling toy model

TL;DR

This paper provides an analytic solution for the transition between superfluid and Bose glass phases in a two-dimensional Bose gas with impurities at zero temperature, revealing phase distinctions and intermediate states.

Contribution

It introduces an analytic expression for the memory function and optical conductivity in a 2D Bose gas with impurities, within the mode-coupling approximation, identifying phase boundaries.

Findings

Identification of superfluid, Bose glass, and intermediate phases.

Analytic expressions for memory function and optical conductivity.

Dependence of phase transition on impurity potential strength.

Abstract

Analytic expression for the memory function and the optical conductivity of the two-dimensional Bose gas with logarithmic interaction at T = 0 in presence of point-like impurities is obtained within the mode-coupling approximation. Depending on the value of a dimensionless combination of the model parameters proportional to the strength of the impurity potential, two different phases are distinguished, viz. the disordered superfluid and insulator (Bose glass), separated by an intermediate (quasi)metal state.