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

Giachetti, Guido; Defenu, Nicoló; Ruffo, Stefano; Trombettoni, Andrea

doi:10.1103/physrevlett.127.156801

Cited by 28 publications

(17 citation statements)

References 81 publications

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“…In Ref. [21] SSB was found to persist in the range 7/4 < σ < 2 up to a finite critical temperature T c , beyond which a quasi-ordered BKT-like phase appears until a larger temperature T BKT . These results are compatible with the application of the Sak criterion with the temperature dependent η sr of the XY model in the SR limit.…”

Section: Introductionmentioning

confidence: 97%

“…In the recent paper [21], the fate of the BKT line of critical points has been discussed. For σ > 2 simple arguments (not directly applicable to σ < 2) show the existence of the BKT transition [22], while what happens for σ < 2 is considerably more subtle.…”

Section: Introductionmentioning

confidence: 99%

“…The comparison between the phase diagrams of Ref. [21] for the 2d classical finite temperature XY model and of Ref. [25] for the 1d quantum zero temperature XXZ model is one of the motivations of the present paper.…”

Section: Introductionmentioning

confidence: 99%

“…IV is devoted to extending the self-consistent approximation to the proper σ < 2 LR regime; while in Sec V we examine the field-theory picture of Ref. [21]. In Sec.…”

Section: Introductionmentioning

confidence: 99%

“…In the present paper, the scenario presented in Ref. [21] for the 2d XY model is analyzed thoughtfully and re-produced using different methods: the low-temperature expansion, an extension of the traditional self-consistent harmonic approximation (SCHA) [22,38,39] to σ < 2 and renormalization group (RG) field theoretical arguments. The difficulties inherent in the use of the Villain approximation for σ < 2 are pointed out and contrasted with the SR case, where, at variance, the 2d Villain and XY model are mappable thorough controllable approximations and lie in the same universality class.…”

Section: Introductionmentioning

confidence: 99%

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$BKT$ transitions in classical and quantum long-range systems

Giachetti¹,

Trombettoni²,

Ruffo³

et al. 2022

Preprint

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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 methods 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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Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…IV is devoted to extending the self-consistent approximation to the proper σ < 2 LR regime; while in Sec V we examine the field-theory picture of Ref. [21]. In Sec.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

$BKT$ transitions in classical and quantum long-range systems

Giachetti¹,

Trombettoni²,

Ruffo³

et al. 2022

Preprint

Self Cite

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Villain model with long-range couplings

Giachetti

Defenu

Ruffo

et al. 2023

J. High Energ. Phys.

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The nearest-neighbor Villain, or periodic Gaussian, model is a useful tool to understand the physics of the topological defects of the two-dimensional nearest-neighbor XY model, as the two models share the same symmetries and are in the same universality class. The long-range counterpart of the two-dimensional XY has been recently shown to exhibit a non-trivial critical behavior, with a complex phase diagram including a range of values of the power-law exponent of the couplings decay, σ, in which there are a magnetized, a disordered and a critical phase [1]. Here we address the issue of whether the critical behavior of the two-dimensional XY model with long-range couplings can be described by the Villain counterpart of the model. After introducing a suitable generalization of the Villain model with long-range couplings, we derive a set of renormalization-group equations for the vortex-vortex potential, which differs from the one of the long-range XY model, signaling that the decoupling of spin-waves and topological defects is no longer justified in this regime. The main results are that for σ < 2 the two models no longer share the same universality class. Remarkably, within a large region of its the phase diagram, the Villain model is found to behave similarly to the one-dimensional Ising model with 1/r2 interactions.

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The breaking of Mermin-Wagner-Hohenberg's theorem for fractional systems

Dartora

2024

Physics Letters A

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

Cited by 28 publications

References 81 publications

$BKT$ transitions in classical and quantum long-range systems

$BKT$ transitions in classical and quantum long-range systems

Villain model with long-range couplings

The breaking of Mermin-Wagner-Hohenberg's theorem for fractional systems

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