Bose Glass in Large N Commensurate Dirty Boson Model

TL;DR

This paper investigates the large N commensurate dirty boson model using renormalization group methods, revealing the absence of a direct phase transition and analyzing disorder effects, correlation functions, and theoretical properties.

Contribution

It provides a perturbative RG analysis of the model, identifies fixed lines and points, and discusses instantons, correlation function distributions, and theorems related to disorder in large N systems.

Findings

Existence of a fixed line with varying disorder in weakly commensurate case

Flow to strong disorder indicating no direct MI-SF transition

Correlation functions follow a log-normal distribution at lowest order

Abstract

The large N commensurate dirty boson model, in both the weakly and strongly commensurate cases, is considered via a perturbative renormalization group treatment. In the weakly commensurate case, there exists a fixed line under RG flow, with varying amounts of disorder along the line. Including 1/N corrections causes the system to flow to strong disorder, indicating that the model does not have a phase transition perturbatively connected to the Mott Insulator-Superfluid (MI-SF) transition. I discuss the qualitative effects of instantons on the low energy density of excitations. In the strongly commensurate case, a fixed point found previously is considered and results are obtained for higher moments of the correlation functions. To lowest order, correlation functions have a log-normal distribution. Finally, I prove two interesting theorems for large N vector models with disorder, relevant to the problem of replica symmetry breaking and frustration in such systems.