Breakdown of self-averaging in the Bose glass

TL;DR

This paper investigates the breakdown of self-averaging in the Bose glass phase of the disordered Bose-Hubbard model using a non-perturbative real-space RG approach, revealing distinct behaviors of mass distribution in different phases.

Contribution

It introduces a real-space block decimation scheme to study the renormalization-group flow of the disorder distribution in the Bose-Hubbard model, highlighting the breakdown of self-averaging.

Findings

Divergent relative variance in the Bose glass indicates non-self-averaging.

Negative mass tails reveal rare superfluid regions.

Explicit phase boundary between Mott insulator and Bose glass established.

Abstract

We study the square-lattice Bose-Hubbard model with bounded random on-site energies at zero temperature. Starting from a dual representation obtained from a strong-coupling expansion around the atomic limit, we employ a real-space block decimation scheme. This approach is non-perturbative in the disorder and enables us to study the renormalization-group flow of the induced random-mass distribution. In both insulating phases, the Mott insulator and the Bose glass, the average mass diverges, signaling short range superfluid correlations. The relative variance of the mass distribution distinguishes the two phases, renormalizing to zero in the Mott insulator and diverging in the Bose glass. Negative mass values in the tail of the distribution indicate the presence of rare superfluid regions in the Bose glass. The breakdown of self-averaging is evidenced by the divergent relative variance and increasingly non-Gaussian distributions. We determine an explicit phase boundary between the Mott insulator and Bose glass.