Berezinskii-Kosterlitz-Thouless transitions in classical and quantum long-range systems

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

doi:10.1103/physrevb.106.014106

Cited by 12 publications

(11 citation statements)

References 72 publications

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“…pCUT [9] energy gap 1.58 ED (this work) fidelity susceptibility 1.592 (1) the critical point. The present exact diagonalization (ED) result (10) is to be compared with this study [9].…”

Section: Methodsmentioning

confidence: 99%

“…5, we present χ F 's scaling plot, (γ − γ c )N 1/ν -N −x χ F , for various transverse field γ and system sizes, (+) N = 28, (×) 30, and ( * ) 32, with the fixed η = 0.5 and α = 2. Here, the scaling parameters are set to γ c = 1.592 (10), and ν = 1; namely, we made a proposition that the criticality belongs to the 2D-Ising universality class [9,22]. This 6), χ F 's scaling plot, (γ − γ c )N 1/ν -N −x χ F , is presented for various system sizes, (+) N = 28, (×) 30, and ( * ) 32.…”

Section: Methodsmentioning

confidence: 99%

“…Our exact diagonalization (ED) result γ c = 1.592(1) [Eq. (10)] obtained via the fidelity susceptibility (4) is to be compared with this pioneering study [9].…”

Section: Transverse-field-driven Criticality For the Fixed Anisotropy...mentioning

confidence: 99%

“…The d-dimensional O(N)-symmetric quantum spin model with the ferromagnetic longrange interactions, J r ∝ −1/r d+σ (r: distance between spins), and the exponent σ has been investigated extensively so far [1,2,3,4,5,6,7,8,9,10,11]; see Ref. [12] for a review.…”

Section: Introductionmentioning

confidence: 99%

“…The interaction parameters, η = 0.5 and α = 2, are the same as those of Fig.3. The scaling parameters are set to γ c = 1.592(10), ν = 1, and x = 1(11); see text for details. The result indicates that the criticality belongs to the 2D-Ising universality class[9,22].…”

mentioning

confidence: 99%

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Fidelity-mediated analysis of the transverse-field XY chain with the long-range interactions: anisotropy-driven multi-criticality

Nishiyama

2021

Eur. Phys. J. B

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The transverse-field XY spin chain with competing antiferromagnetic long-range interactions, J r ∝ 1/r α (r: distance between spins), and the exponent α was investigated numerically. The main concern is to clarify the character of the transversefield-driven phase transition for the small-α regime around the XX-symmetric point, η = 0 (η: XY -anisotropy parameter). To cope with the negative-sign problem, we employed the exact-diagonalization method, which enables us to evaluate the fidelity susceptibility χ F . Because the fidelity susceptibility does not assume any order parameter after a phase transition, it detects the multi-criticality around the XXsymmetric point in a systematic manner. As a preliminary survey, with η = 0.5 and α = 2 fixed, we made the scaling analysis of χ F . The scaling behavior of χ F shows that the transverse-field-driven phase transition belongs to the 2D-Ising universality class. Thereby, with the properly crossover-scaled η, the χ F data is cast into the crossover scaling formula for the small-α regime. The multi-critical exponents fed into the scaling formula are argued through referring to related studies.

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“…pCUT [9] energy gap 1.58 ED (this work) fidelity susceptibility 1.592 (1) the critical point. The present exact diagonalization (ED) result (10) is to be compared with this study [9].…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

“…Our exact diagonalization (ED) result γ c = 1.592(1) [Eq. (10)] obtained via the fidelity susceptibility (4) is to be compared with this pioneering study [9].…”

Section: Transverse-field-driven Criticality For the Fixed Anisotropy...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Fidelity-mediated analysis of the transverse-field XY chain with the long-range interactions: anisotropy-driven multi-criticality

Nishiyama

2021

Eur. Phys. J. B

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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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