Berezinskii-Kosterlitz-Thouless Phase Transitions with Long-Range Couplings

The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a quasiordered phase, characterized by a power-law scaling of the correlation functions at low temperature, is disrupted by the proliferation of topological excitations above the critical temperature $T_{\mathrm{BKT}}$. In this Letter, we consider the effect of long-range decaying couplings $\sim r^{-2-\sigma }$ on the BKT transition. After pointing out the relevance of this nontrivial problem, we discuss the phase diagram, which is far richer than the corresponding short-range one. It features—for $7/4<\sigma <2$—a quasiordered phase in a finite temperature range $T_c<T<T_{\mathrm{BKT}}$, which occurs between a symmetry broken phase for $T<T_c$ and a disordered phase for $T>T_{\mathrm{BKT}}$. The transition temperature $T_c$ displays unique universal features quite different from those of the traditional, short-range $XY$ model. Given the universal nature of our findings, they may be observed in current experimental realizations in 2D atomic, molecular, and optical quantum systems.