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BKT transitions in classical and quantum long-range systems

In the past decades considerable efforts have been made in order to understand the critical features of both classical and quantum long-range interacting models. The case of the Berezinskii - Kosterlitz - Thouless (BKT) universality class, as in the $2d$ classical $XY$ model, is considerably complic...

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Hauptverfasser: Giachetti, Guido (VerfasserIn) , Trombettoni, Andrea (VerfasserIn) , Ruffo, Stefano (VerfasserIn) , Defenu, Nicolò (VerfasserIn)
Dokumenttyp: Article (Journal) Kapitel/Artikel
Sprache:Englisch
Veröffentlicht: 2022
In: Arxiv
Year: 2022, Pages: 1-15
DOI:10.48550/arXiv.2201.03650
Online-Zugang:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.48550/arXiv.2201.03650
Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2201.03650
Volltext
Verfasserangaben:Guido Giachetti, Andrea Trombettoni, Stefano Ruffo, Nicolò Defenu

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520 |a In the past decades considerable efforts have been made in order to understand the critical features of both classical and quantum long-range interacting models. The case of the Berezinskii - Kosterlitz - Thouless (BKT) universality class, as in the $2d$ classical $XY$ model, is considerably complicated by the presence, for short-range interactions, of a line of renormalization group fixed points. In this paper we discuss a field theoretical treatment of the $2d$ $XY$ model with long-range couplings and we compare it with results from the self-consistent harmonic approximation. Both these methods lead to a rich phase diagram, where both power-law BKT scaling and spontaneous symmetry breaking appear for the same (intermediate) decay rates of long-range interactions. The method is also applied to the long-range quantum $XXZ$ spin chain at zero temperature. We discuss the relation between the phase diagrams of the two models and we give predictions about the scaling of the order parameter of the quantum chain close to the transition. Finally, we discuss the Villain approximation for the $2d$ $XY$ model and we show how, in the long-range regime, it fails to reproduce the correct critical behavior. 
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