Duality-mediated critical amplitude ratios for the (2 + 1)-dimensional S = 1XY model

Yoshihiro Nishiyama

doi:10.1140/epjb/e2017-80286-1

Duality-mediated critical amplitude ratios for the (2 + 1)-dimensional S = 1XY model

Yoshihiro Nishiyama

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

The phase transition for the (2 + 1)-dimensional spin-S = 1XY model was investigated numerically. Because of the boson-vortex duality, the spin stiffness ρ_s in the ordered phase and the vortex-condensate stiffness ρ_v in the disordered phase should have a close relationship. We employed the exact diagonalization method, which yields the excitation gap directly. As a result, we estimate the amplitude ratios ρ_s,v/Δ (Δ: Mott insulator gap) by means of the scaling analyses for the finite-size cluster with N ≤ 22 spins. The ratio ρ_s/ρ_v admits a quantitative measure of deviation from selfduality.

Original language	English
Article number	173
Journal	European Physical Journal B
Volume	90
Issue number	9
DOIs	https://doi.org/10.1140/epjb/e2017-80286-1
Publication status	Published - Sep 1 2017

Keywords

Statistical and Nonlinear Physics

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Condensed Matter Physics

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10.1140/epjb/e2017-80286-1

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abstract = "The phase transition for the (2 + 1)-dimensional spin-S = 1XY model was investigated numerically. Because of the boson-vortex duality, the spin stiffness ρs in the ordered phase and the vortex-condensate stiffness ρv in the disordered phase should have a close relationship. We employed the exact diagonalization method, which yields the excitation gap directly. As a result, we estimate the amplitude ratios ρs,v/Δ (Δ: Mott insulator gap) by means of the scaling analyses for the finite-size cluster with N ≤ 22 spins. The ratio ρs/ρv admits a quantitative measure of deviation from selfduality.",

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N2 - The phase transition for the (2 + 1)-dimensional spin-S = 1XY model was investigated numerically. Because of the boson-vortex duality, the spin stiffness ρs in the ordered phase and the vortex-condensate stiffness ρv in the disordered phase should have a close relationship. We employed the exact diagonalization method, which yields the excitation gap directly. As a result, we estimate the amplitude ratios ρs,v/Δ (Δ: Mott insulator gap) by means of the scaling analyses for the finite-size cluster with N ≤ 22 spins. The ratio ρs/ρv admits a quantitative measure of deviation from selfduality.

AB - The phase transition for the (2 + 1)-dimensional spin-S = 1XY model was investigated numerically. Because of the boson-vortex duality, the spin stiffness ρs in the ordered phase and the vortex-condensate stiffness ρv in the disordered phase should have a close relationship. We employed the exact diagonalization method, which yields the excitation gap directly. As a result, we estimate the amplitude ratios ρs,v/Δ (Δ: Mott insulator gap) by means of the scaling analyses for the finite-size cluster with N ≤ 22 spins. The ratio ρs/ρv admits a quantitative measure of deviation from selfduality.

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