Doubling of Entanglement Spectrum in Tensor Renormalization Group
Doubling of Entanglement Spectrum in Tensor Renormalization Group
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DOI：
10.1103/physrevb.89.075116
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发表时间：
2013-06
影响因子：
3.7
通讯作者：
H. Ueda;K. Okunishi;T. Nishino
中科院分区：
文献类型：
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作者：
H. Ueda;K. Okunishi;T. Nishino
研究了二维经典顶点模型的HOTRG-张量重整化群(RG)方法结合高阶奇异值分解的纠缠谱。在非临界区，解释了与RG变换相关的纠缠谱可以用角点转移矩阵的谱的“加倍”来描述。然后，我们通过HOTRG计算证明了正方形晶格伊辛模型的倍增实际上发生了，直到D=，其中D是张量的截止维度。在临界点，我们还发现在纠缠熵中出现了非平凡的D标度行为。我们还提到了一维量子系统的HOTRG。
We investigate the entanglement spectrum in HOTRG —tensor renormalization group (RG) method combined with the higher order singular value decomposition— for two-dimensional (2D) classical vertex models. In the off-critical region, it is explained that the entanglement spectrum associated with the RG transformation is described by ‘doubling’ of the spectrum of a corner transfer matrix. We then demonstrate that the doubling actually occurs for the square-lattice Ising model by HOTRG calculations up to D = 64, where D is the cut-off dimension of tensors. At the critical point, we also find that a non-trivial D scaling behavior appears in the entanglement entropy. We mention about the HOTRG for the 1D quantum system as well.