We propose a hole decomposition scheme to exactly solve a class of spin-1 quantum Ising models with transverse or longitudinal single-ion anisotropy. In this scheme, the spin-1 model is mapped onto a family of the $S=1/2$ transverse Ising models, characterized by the total number of holes. A recursion formula is derived for the partition function based on the reduced $S=1/2$ Ising model. This simplifies greatly the summation over all the hole configurations. It allows the thermodynamic quantities to be rigorously determined in the thermodynamic limit. The ground state phase diagram is determined for both the uniform and dimerized spin chains. The corresponding thermodynamic properties are calculated and discussed.
Fractional magnetization plateaux of the spin-1/2 Heisenberg orthogonal-dimer chain revisited: strong-coupling approach developed from the exactly solved Ising-Heisenberg model
Exact evidence for the spontaneous antiferromagnetic long-range order in the two-dimensional hybrid model of localized Ising spins and itinerant electrons
Topological Kondo effect in star junctions of Ising magnetic chains. Exact solution
本文对描述$M$量子临界伊辛链星形结模型的Bethe不等式提出一个猜想。对于$M>3$，这种模型表现出所谓的拓扑近藤效应[B. Beri和N. R. Cooper，Phys. Rev. Lett. { \bf 109}，156803（2012）]中所述的与结处存在马约拉纳零能模式有关的缺陷。这些模式是一个拓扑性质，他们非本地编码的SO（M）的“自旋”，这是由链的集体激发屏蔽。对于一定的$M$值，该模型等价于具有已知精确解的Kondo模型。这些情况被用来检查猜想的有效性。结果表明，该模型的行为不同的$M$偶数和奇数，在前一种情况下，该模型具有费米液体和后一种情况对应于一个非费米液体红外固定点。
我们研究了在远低于能隙的温度下，横向场中量子伊辛链顺磁相的低频自旋磁化率。我们发现，虚部占主导地位的罕见的量子过程中，准粒子的数量变化的奇数。我们得到的NMR弛豫速率在低温极限的可积模型与最近邻伊辛相互作用的精确结果，并推导出精确的通用标度结果适用于通用伊辛链附近的量子临界点。这些结果解决了用不同的实验探针测量的伊辛链系统CoNb $_{2}$ O $_{6}$的量子无序顺磁相的能量尺度之间的某些差异。
