Quantum critical dynamics of the two-dimensional Bose gas

TL;DR

This paper develops a theoretical framework for the quantum critical dynamics of a two-dimensional Bose gas at finite temperature, revealing strong collective effects despite weak pairwise interactions, with applications to experimental spin gap systems.

Contribution

It introduces a leading-order theory for the quantum critical dynamics of the 2D Bose gas, highlighting strong collective behavior and providing a numerical classical model for analysis.

Findings

Strong collective dynamics emerge despite weak pairwise interactions.

The effective classical model captures the critical behavior.

Applications to spin gap antiferromagnets demonstrate experimental relevance.

Abstract

The dilute, two-dimensional Bose gas exhibits a novel regime of relaxational dynamics in the regime k_B T > |\mu| where T is the absolute temperature and \mu is the chemical potential. This may also be interpreted as the quantum criticality of the zero density quantum critical point at \mu=0. We present a theory for this dynamics, to leading order in 1/\ln (\Lambda/ (k_B T)), where \Lambda is a high energy cutoff. Although pairwise interactions between the bosons are weak at low energy scales, the collective dynamics are strongly coupled even when \ln (\Lambda/T) is large. We argue that the strong-coupling effects can be isolated in an effective classical model, which is then solved numerically. Applications to experiments on the gap-closing transition of spin gap antiferromagnets in an applied field are presented.