Quantum critical dynamics of the two-dimensional Bose gas

The dilute, two-dimensional Bose gas exhibits a novel regime of relaxational dynamics in the regime $k_{B}T\gtrsim \mid \mu \mid$ 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 dynamic, to leading order in $1∕\ln [\Lambda ∕(k_{B}T\left)\right]$, 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.