Topological basis realization associated with Hermitian and non-Hermitian Heisenberg XXZ model
Topological basis realization associated with Hermitian and non-Hermitian Heisenberg XXZ model
复制标题
与厄米和非厄米海森堡 XXZ 模型相关的拓扑基实现
DOI：
10.1209/0295-5075/122/50004
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发表时间：
2018-06-01
期刊：
影响因子：
1.8
通讯作者：
Xue, Kang
中科院分区：
文献类型：
--
作者：
Gong, Shiyao;Wang, Gangcheng;Xue, Kang
我们研究了基于Temperley-Lieb代数的矩阵表示的Hermitian和非Hermitian海森堡XXZ模型的拓扑基实现。结果表明，拓扑空间是由与Temperley-Lieb代数相关的拓扑基所张成的。当q变形参数q为复数时，对应的模型为非厄米特XXZ模型。真实的q对应于厄米坦情形。这两种情况下的拓扑基实现构造的Temperley-Lieb代数的矩阵表示。然后研究了拓扑基和基态的性质。特别地，我们详细研究了四量子比特海森堡XXZ模型。对q是单位根的情形也作了一些讨论。
We investigate the topological basis realization associated with the Hermitian and non-Hermitian Heisenberg XXZ model based on the matrix representation of the Temperley-Lieb algebra. The results show that the topological space is spanned by the topological basis associated with the Temperley-Lieb algebra. When the q-deformed parameter q is a complex number and , the corresponding model is the non-Hermitian XXZ model. The real q corresponds to the Hermitan case. The topological basis realization for these two cases is constructed by means of matrix representation of the Temperley-Lieb algebra. Then the properties of the topological basis and ground state are studied. Particularly, the four-qubit Heisenberg XXZ model is investigated in detail. We also give some discussions on the case in which q is a root of unity.