Berezinskii-Kosterlitz-Thouless transitions in an easy-plane ferromagnetic superfluid

A two-dimensional spin-1 Bose gas exhibits two Berezinskii-Kosterlitz-Thouless (BKT) transitions in the easy-plane ferromagnetic phase. The higher-temperature transition is associated with superfluidity of the mass current determined predominantly by a single spin component. The lower-temperature transition is associated with superfluidity of the axial spin current, quasi-long-range order of the transverse spin density, and binding of polar-core spin vortices (PCVs). Above the spin BKT temperature, the component circulations that make up each PCV spatially separate, suggesting possible deconfinement analogous to quark deconfinement in high-energy physics. Intercomponent interactions give rise to superfluid drag between the spin components, which we calculate analytically at zero temperature. We present the mass and spin superfluid phase diagram as a function of quadratic Zeeman energy q. At q = 0 the system is in an isotropic spin phase with SO(3) symmetry. Here the fluid response exhibits a system size dependence, suggesting the absence of a BKT transition. Despite this, for finite systems the decay of spin correlations changes from exponential to algebraic as the temperature is decreased.