Ising-criticality-driven deconfinement of vortices in a spin-orbit coupled Bose gas

Spin-orbit coupling in a two-dimensional Bose gas is known to lead to an Ising symmetry broken phase where the Bosons condense at finite momentum. 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 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 using a Monte Carlo simulation which shows the disappearance of superfluid stiffness near an Ising transition. Additionally, we find that the Ising phase transition becomes first order and we justify this claim with a variational approximation.