Persistence of the Berezinskii-Kosterlitz-Thouless transition with long-range couplings

TL;DR

This paper demonstrates that the Berezinskii-Kosterlitz-Thouless transition persists in the XY model with long-range interactions, showing stability of topological phase transitions under algebraically decaying couplings.

Contribution

It provides a comprehensive analysis combining Landau-Peierls arguments and renormalization group methods to show the BKT transition's robustness with long-range interactions.

Findings

BKT transition persists for all long-range exponents.

Long-range interactions stabilize the topological phase.

No direct transition from magnetized to disordered phase.

Abstract

The Berezinskii-Kosterlitz-Thouless (BKT) transition is an archetypal example of a topological phase transition, which is driven by the proliferation of vortices. In this Letter, we analyze the persistence of the BKT transition in the XY model under the influence of long-range algebraically decaying interactions of the form $\sim 1/{r^{2+\sigma}}$. The model hosts a magnetized low temperature phase for sufficiently small $\sigma$. Crucially, in the presence of long-range interactions, spin waves renormalize the interaction between vortices, which stabilizes the BKT transition. As a result, we find that there is no direct transition from the magnetized to the disordered phase and that the BKT transition persists for arbitrary long-range exponents, which is distinct from previous results. We use both Landau-Peierls-type arguments and renormalization group calculations - including a coupling between spin wave and topological excitations - and obtain similar results. We emphasize that Landau-Peierls-type arguments are a powerful tool for analyzing continuous spin models. We discuss the relevance of our findings for current Rydberg atom experiments, and highlight the importance of long-range couplings for other types of topological defects.