PMID: 22587032May 17, 2012Paper

Holographic entanglement entropy in Suzuki-Trotter decomposition of spin systems

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Hiroaki Matsueda

Abstract

In quantum spin chains at criticality, two types of scaling for the entanglement entropy exist: one comes from conformal field theory (CFT), and the other is for entanglement support of matrix product state (MPS) approximation. On the other hand, the quantum spin-chain models can be mapped onto two-dimensional (2D) classical ones by the Suzuki-Trotter decomposition. Motivated by the scaling and the mapping, we introduce information entropy for 2D classical spin configurations as well as a spectrum, and examine their basic properties in the Ising and the three-state Potts models on the square lattice. They are defined by the singular values of the reduced density matrix for a Monte Carlo snapshot. We find scaling relations of the entropy compatible with the CFT and the MPS results. Thus, we propose that the entropy is a kind of "holographic" entanglement entropy. At T(c), the spin configuration is fractal, and various sizes of ordered clusters coexist. Then, the singular values automatically decompose the original snapshot into a set of images with different length scales, respectively. This is the origin of the scaling. In contrast to the MPS scaling, long-range spin correlation can be described by only few singular values. Fur...Continue Reading

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May 21, 2010·Physical Review Letters·R ThomaleB Andrei Bernevig

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Citations

Sep 19, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yoichiro HashizumeMasuo Suzuki
Jan 14, 2017·Physical Review. E·Ching Hua LeeHiroaki Matsueda
Nov 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hiroaki Matsueda, Dai Ozaki

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