论文标题
$（2+1）$ d超级氟化物 - 绝缘体过渡器的单位 - 量价量子外部场导致的过量能源成本的关键性
Criticality of the excess energy cost due to the unit-flux-quantum external field for the $(2+1)$D superfluid-insulator transition
论文作者
论文摘要
二维（$ 2 $ d）旋转-S = 1 $ $ xy $型号是数值研究的，以实现$（2+1）$ d superfluid-mott-mott-mott-mott-Munt-mimott-Mimott-Min-Min-MiT-MiT-mi（SF-MI）过渡。扩展了交互参数，以抑制校正以缩小有限尺寸的缩放。因此，通过将相位因子$ e^{ix_ {ij}} $（$ ϕ__ {ij {ij} $：$ i $和$ j $ j $ j $ j $和$ j $ j $ j $ j $ j $ j $ n opplitudes纳入跳台，将单位通量量子的外场（$φ=2π$）应用于2D群集。利用优势，确切的二进制方法使我们能够处理这种复杂值的矩阵元素，因此我们评估了由于磁通量$φ=2π=2π$在SF（$ xy $）阶段中的多余能量成本$ΔE（2π）$。结果，我们发现振幅比$ρ_s /δe（2π）$（$ρ_s$：旋转刚度）在临界点附近是有意义的，在SF相侧表现出显着的高原。估计高原高度，并与相关研究进行了比较。
The two-dimensional ($2$D) spin-$S=1$ $XY$ model was investigated numerically as a realization of the $(2+1)$D superfluid-Mott-insulator (SF-MI) transition. The interaction parameters are extended so as to suppress corrections to finite-size scaling. Thereby, the external field of a unit flux quantum ($Φ=2π$) is applied to the 2D cluster by incorporating the phase factor $e^{iϕ_{ij}}$ ($ϕ_{ij}$: gauge angle between the $i$ and $j$ sites) into the hopping amplitudes. Taking the advantage in that the exact-diagonalization method allows us to treat such a complex-valued matrix element, we evaluated the excess energy cost $ΔE(2π)$ due to the magnetic flux $Φ=2π$ explicitly in the SF ($XY$) phase. As a result, we found that the amplitude ratio $ρ_s / ΔE(2π)$ ($ρ_s$: spin stiffness) makes sense in proximity to the critical point, exhibiting a notable plateau in the SF-phase side. The plateau height is estimated, and compared to the related studies.
