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arXiv · 1710.02927

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

Y. Nishiyama
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Abstract

The phase transition for the $(2+1)$-dimensional spin-$S=1$ $XY$ 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 $N \le 22$ spins. The ratio $ρ_s/ρ_v$ admits a quantitative measure of deviation from selfduality.

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Y. Nishiyama. 2017-10-09. Duality-mediated critical amplitude ratios for the $(2+1)$-dimensional $S=1$ $XY$ model. https://doi.org/10.1140/epjb%2Fe2017-80286-1

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