Simulations of Disordered Bosons on Hyper-Cubic Lattices

TL;DR

This paper investigates the critical behavior of disordered bosonic systems at low temperatures using simulations of the disordered Bose-Hubbard model, introducing an efficient algorithm and modifications to improve computational performance.

Contribution

It presents a novel application of a (3+1)D link-current model with a worm algorithm to study the Bose-glass to superfluid transition, including modifications for enhanced efficiency.

Findings

Distribution of superfluid stiffness over disorder realizations calculated

Modified link-current Hamiltonian improves numerical efficiency

Universal critical behavior captured by the model

Abstract

We address computational issues relevant to the study of disordered quantum mechanical systems at very low temperatures. As an example we consider the disordered Bose- Hubbard model in three dimensions directly at the Bose-glass to superfluid phase transition. The universal aspects of the critical behaviour are captured by a (3 + 1) dimensional link-current model for which an efficient 'worm' algorithm is known. We present a calculation of the distribution of the superfluid stiffness over the disorder realizations, outline a number of important considerations for performing such estimates, and suggest a modification of the link-current Hamiltonian that improves the numerical efficiency of the averaging procedure without changing the universal properties of the model.