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Persistence of the Berezinskii-Kosterlitz-Thouless Transition with Long-Range Couplings

Luis Walther1,2,*, Josef Willsher1,3,2, and Johannes Knolle1,3,4

  • *Contact author: lwalther@pks.mpg.de
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Phys. Rev. Lett. 136, 227102 – Published 5 June, 2026

DOI: https://doi.org/10.1103/9y2v-ybdb

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 ∼1/r2+σ. The model hosts a magnetized low temperature phase for sufficiently small σ. 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. The key methodological advance is the inclusion of coupling between spin wave and topological excitations. We do this by developing Landau-Peierls–type arguments and using higher-order renormalization group calculations, obtaining compatible 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.

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Phys. Rev. Lett. 136, 227102– Published 5 June, 2026
  • Received 21 November 2025
  • Accepted 15 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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