The fate of exotic spin liquid states with fractionalized excitations at finite temperature ($T$) is of great interest, since signatures of fractionalization manifest in finite-temperature ($T$) dynamics in real systems, above the tiny magnetic ordering scales. Here, we study a Jordan–Wigner (JW) fermionized Kitaev spin liquid at finite $T$ employing combined exact diagonalization and Monte Carlo simulation methods. We uncover $\left(i\right)$ checkerboard or stripy-ordered flux crystals depending on density of flux, and $\left(ii\right)$ establish, surprisingly, that: $\left(a\right)$ the finite-$T$ version of the $T=0$ transition from a gapless to gapped phases in the Kitaev model is a Mott transition of the fermions, belonging to the two-dimensional Ising universality class. These transitions correspond to a topological transition between a string condensate and a dilute closed string state $\left(b\right)$ the Mott “insulator” phase is a precise realization of Laughlin’s gossamer (here, $p$-wave) superconductor (g-SC), and $\left(c\right)$ the Kitaev Toric Code phase (TC) is adiabatically connected to the g-SC, and is a fully Gutzwiller-projected fermi sea of JW fermions. These findings establish the finite-$T$ quantum spin liquid phases in the $d=2$ to be hidden Fermi liquid(s) of neutral fermions.

在有限温度下具有分次激发的奇异自旋液态的命运（$Ť$）非常受关注，因为分馏的特征体现在有限温度（$Ť$）在微小磁阶以上的真实系统中的动力学。在这里，我们研究有限温度下约旦-维格纳（JW）费米化的Kitaev自旋液体$Ť$采用精确对角线化和蒙特卡洛模拟方法相结合。我们发现$（\mathrm{一世}）$ 取决于通量密度的棋盘状或条状有序通量晶体，以及 $（\mathrm{一世}\mathrm{一世}）$ 令人惊讶地确定： $（\mathrm{一种}）$ 有限的$Ť$ 版本 $Ť=0$Kitaev模型中从无缝隙相过渡到有缝隙相的过程是费米子的莫特跃迁，属于二维Ising普适性类。这些过渡对应于管柱冷凝物和稀闭管柱状态之间的拓扑过渡$（b）$ Mott的“绝缘体”阶段是对Laughlin的游丝的精确实现（在这里， $p$-波）超导体（g-SC），以及 $（C）$Kitaev Toric Code阶段（TC）绝热地连接到g-SC，并且是完全由Gutzwiller投射的JW费米子费米海。这些发现建立了有限的$Ť$ 量子自旋液相 $d=\mathrm{2个}$被隐藏的中性费米液体。