Topological defects and the superfluid transition of the $s=1$ spinor condensate in two dimensions

TL;DR

This paper investigates the topological defects and phase transitions in a two-dimensional $s=1$ spinor Bose condensate, revealing a nematic superfluid phase with algebraic order and characterizing the Kosterlitz-Thouless transition driven by half-vortex unbinding.

Contribution

It corrects previous studies on topological defects and demonstrates the instability of the polar condensate at finite temperature, identifying a novel nematic superfluid phase with unique transition properties.

Findings

Polar condensate is unstable at finite temperature in 2D.

Existence of a nematic or paired superfluid phase with algebraic order.

Confirmation of the universal $8 T_c / \pi$ stiffness jump at the transition.

Abstract

The $s=1$ spinor Bose condensate at zero temperature supports ferromagnetic and polar phases that combine magnetic and superfluid ordering. We analyze the topological defects of the polar condensate, correcting previous studies, and show that the polar condensate in two dimensions is unstable at any finite temperature; instead there is a nematic or paired superfluid phase with algebraic order in $\exp(2 i \theta)$, where $\theta$ is the superfluid phase, and no magnetic order. The Kosterlitz-Thouless transition out of this phase is driven by unbinding of half-vortices (the spin-disordered version of the combined spin and phase defects found by Zhou), and the anomalous universal $8 T_c / \pi$ stiffness jump at the transition is confirmed in numerical simulations. The anomalous stiffness jump is a clear experimental signature of this phase and the corresponding phase transition.