Ising criticality can drive vortex deconfinement in a spin-orbit coupled Bose gas

Spin-orbit coupling in Bose gases is known to lead to an Ising-symmetry-broken phase where the bosons condense at one of two nonzero momenta. In two dimensions, the finite momentum of the order parameter allows vortex-antivortex pairs that are typically bound in the superfluid phase to freely separate along Ising domain walls. This non-trivial interaction between the superfluid and the Ising order suggests that the critical fluctuations near an Ising transition could drive a Berezinskii-Kosterlitz-Thouless transition of the superfluid. We present numerical evidence of this phenomenon using a Monte Carlo simulation that shows the disappearance of superfluid stiffness near an Ising transition. Additionally, we find numerical evidence that the Ising phase transition becomes first order and we justify this claim with a variational approximation.