Exactly Solvable Fermion Chain Describing a v=1/3 Fractional Quantum Hall State
Exactly Solvable Fermion Chain Describing a v=1/3 Fractional Quantum Hall State
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DOI：
10.1103/physrevlett.109.016401
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发表时间：
2012-07-02
影响因子：
8.6
通讯作者：
Bergholtz, Emil J.
中科院分区：
文献类型：
--
作者：
Nakamura, Masaaki;Wang, Zheng-Yuan;Bergholtz, Emil J.
我们引入了一个精确可解的费米子链，它描述了一个v = 1/3的分数量子霍尔（HHH）状态超过薄环面限制。我们的模型的基态被证明是唯一的每个质心部门，它有一个矩阵产品表示，使我们能够准确地计算序参数，相关函数，和纠缠谱。我们的模型的基态表现出惊人的相似性BCS波函数和量子自旋-1链。利用矩阵乘积的变分方法，我们解析地计算了激发能隙和在基态下的压缩性消失。我们还证明了上述结果与v = 1/2玻色-OH态有关。
We introduce an exactly solvable fermion chain that describes a v = 1/3 fractional quantum Hall (FQH) state beyond the thin-torus limit. The ground state of our model is shown to be unique for each center-of-mass sector, and it has a matrix product representation that enables us to exactly calculate order parameters, correlation functions, and entanglement spectra. The ground state of our model shows striking similarities with the BCS wave functions and quantum spin-1 chains. Using the variational method with matrix product ansatz, we analytically calculate excitation gaps and vanishing of the compressibility expected in the FQH state. We also show that the above results can be related to a v = 1/2 bosonic FQH state.