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arXiv · 1306.6829

Doubling of Entanglement Spectrum in Tensor Renormalization Group

Hiroshi Ueda·Kouichi Okunishi·Tomotoshi Nishino
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Abstract

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.

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Hiroshi Ueda, Kouichi Okunishi, Tomotoshi Nishino. 2014-01-31. Doubling of Entanglement Spectrum in Tensor Renormalization Group. https://doi.org/10.1103/physrevb.89.075116

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