随机量子海森堡磁铁中的自旋液体到自旋玻璃交叉
Spin liquid to spin glass crossover in the random quantum Heisenberg magnet
摘要：
本文研究了具有均方根强度$J$的海森堡交换作用的全对全和随机SU（$M$）自旋。$M \rightarrow \infty$模型具有自旋液体基态，自旋子服从Sachdev-Ye-Kitaev（SYK）模型的方程。对含$S=1/2$自旋的SU（2）模型的数值研究表明，在基态下存在自旋玻璃有序，但在中频自旋谱中也显示出SYK自旋液体行为.我们采用$1/M$展开来描述从分数化的费米子自旋到具有弱$q_{EA}$自旋玻璃序的限制自旋玻璃态的跃迁。SYK自旋液体行为持续下降到频率$ω_\ast \sim J q_{EA}$，并且对于$ω< ω_\ast$，谱密度在$ω$中是线性的，因此淬灭自旋液体的广泛零温度熵。线性$ω$谱定性地类似于先前使用玻色子自旋获得的大$q_{EA}$。我们认为，广泛的SYK自旋液体熵转化为$T \rightarrow 0$广泛的复杂性的自旋玻璃状态。
英文摘要：
We study quantum SU($M$) spins with all-to-all and random Heisenberg exchange interactions of root-mean-square strength $J$. The $M \rightarrow \infty$ model has a spin liquid ground state with the spinons obeying the equations of the Sachdev-Ye-Kitaev (SYK) model. Numerical studies of the SU(2) model with $S=1/2$ spins show spin glass order in the ground state, but also display SYK spin liquid behavior in the intermediate frequency spin spectrum. We employ a $1/M$ expansion to describe the crossover from fractionalized fermionic spinons to a confining spin glass state with weak spin glass order $q_{EA}$. The SYK spin liquid behavior persists down to a frequency $ω_\ast \sim J q_{EA}$, and for $ω< ω_\ast$, the spectral density is linear in $ω$, thus quenching the extensive zero temperature entropy of the spin liquid. The linear $ω$ spectrum is qualitatively similar to that obtained earlier using bosonic spinons for large $q_{EA}$. We argue that the extensive SYK spin liquid entropy is transformed as $T \rightarrow 0$ to an extensive complexity of the spin glass state.
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