Identifying topological order by entanglement entropy
Identifying topological order by entanglement entropy
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DOI：
10.1038/nphys2465
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发表时间：
2012-12-01
期刊：
影响因子：
19.6
通讯作者：
Balents, Leon
中科院分区：
文献类型：
--
作者：
Jiang, Hong-Chen;Wang, Zhenghan;Balents, Leon
拓扑相是物质的独特状态，它包含了长程量子纠缠和带有分数量子统计的奇异激发。在这里，我们报道了一种实用的方法，通过使用密度矩阵重整化群(DMRG)精确计算拓扑纠缠熵来识别任意现实模型中的拓扑相。我们认为，DMRG算法系统地从拓扑阶段的准简并基态中选择一个最小纠缠态。这一趋势既解释了我们方法的成功，也解释了在以前的DMRG拓扑相研究中没有基态简并。当圆柱体的周长约为关联长度的10倍时，我们通过计算几个微观模型的拓扑纠缠熵，证明了该方法的有效性，其精度达到103量级。作为例子，我们明确地证明了Kagome晶格上量子S=1/2反铁磁体的基态是拓扑自旋液体，并强烈地约束了识别这一相物质的条件。
Topological phases are unique states of matter that incorporate long-range quantum entanglement and host exotic excitations with fractional quantum statistics. Here we report a practical method to identify topological phases in arbitrary realistic models by accurately calculating the topological entanglement entropy using the density matrix renormalization group (DMRG). We argue that the DMRG algorithm systematically selects a minimally entangled state from the quasi-degenerate ground states in a topological phase. This tendency explains both the success of our method and the absence of ground-state degeneracy in previous DMRG studies of topological phases. We demonstrate the effectiveness of our procedure by obtaining the topological entanglement entropy for several microscopic models, with an accuracy of the order of 10 3, when the circumference of the cylinder is around ten times the correlation length. As an example, we definitively show that the ground state of the quantum S = 1/2 antiferromagnet on the kagome lattice is a topological spin liquid, and strongly constrain the conditions for identification of this phase of matter.