Accurate determination of tensor network state of quantum lattice models in two dimensions
Accurate determination of tensor network state of quantum lattice models in two dimensions
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DOI：
10.1103/physrevlett.101.090603
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发表时间：
2008-08-29
影响因子：
8.6
通讯作者：
Xiang, T.
中科院分区：
文献类型：
--
作者：
Jiang, H. C.;Weng, Z. Y.;Xiang, T.
我们提出了一种利用二维张量网络波函数精确计算基态物理量的数值方法。张量网络波函数由迭代投影法确定，该方法利用量子算符的Trotter-Suzuki分解公式和矩阵的奇异值分解。用粗粒张量重整化群方法计算了波函数的范数和物理可观测量的期望值。我们的方法允许在热力学极限下精确而有效地处理具有高成键自由度(如D=8)的张量网络波函数。对于蜂窝晶格上的海森堡模型，我们对基态能量和交错磁化强度的计算结果与量子蒙特卡罗等方法得到的结果符合得很好。
We have proposed a novel numerical method to calculate accurately physical quantities of the ground state using the tensor network wave function in two dimensions. The tensor network wave function is determined by an iterative projection approach which uses the Trotter-Suzuki decomposition formula of quantum operators and the singular value decomposition of matrix. The norm of the wave function and the expectation value of a physical observable are evaluated by a coarse-grain tensor renormalization group approach. Our method allows a tensor network wave function with a high bond degree of freedom (such as D = 8) to be handled accurately and efficiently in the thermodynamic limit. For the Heisenberg model on a honeycomb lattice, our results for the ground state energy and the staggered magnetization agree well with those obtained by the quantum Monte Carlo and other approaches.