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arXiv · 1412.5285

Global quantum discord in infinite quantum spin chains

Zhao-Yu Sun·Yan-E Liao·Bin Guo·Hai-Lin Huang·Duo Zhang·Jian Xu·Bi-Fu Zhan·Yu-Yin Wu·Hong-Guang Cheng·Guo-Zhi Wen·Chao Fang·Cheng-Bo Duan·Bo Wang
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Abstract

In this paper, we study global quantum discord (GQD) in infinite-size spin chains. For this purpose, in the framework of matrix product states (MPSs), we propose an effective procedure to calculate GQD (denoted as Gn) for consecutive n-site subchains in infinite chains. For a spin-1/2 three-body interaction model, whose ground state can be exactly expressed as MPSs, We use the procedure to study Gn with n up to $24$. Then for a spin-1/2 XXZ chain, we firstly use infinite time-evolving block decimation (iTEBD) algorithm to obtain the approximate wavefunction in the from of MPSs, and then figure out Gn with n up to $18$. In both models, Gn shows an interesting linear growth as the increase of n, that is, Gn = k*n+b. Moreover, in non-critical regions the slope $k$ of Gn converges very fast, while in critical regions it converges relatively slow, and the behaviors are explained in a clear physical picture with the short-range and long-range correlations. Based on these results, we propose to use Gn/n to describe the global correlations in infinite chains. Gn/n has twofold physical meanings. Firstly, it can be regarded as "global discord per site", very similar to "energy per site" or "magnetization per site" in quantum magnetic systems. Secondly, Gn/n (when n is large enough) describes the quantum correlation between a single site and an (n-1)-site block. Then we successfully apply our theory to an exactly soluble infinite-size spin XY chain which is beyond the matrix product formula, and the Hamiltonian can reduce to the transverse-field Ising model and the XX model. The relation between GQD and quantum phase transitions in these models is discussed.

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Zhao-Yu Sun, Yan-E Liao, Bin Guo, Hai-Lin Huang, Duo Zhang, Jian Xu, Bi-Fu Zhan, Yu-Yin Wu, Hong-Guang Cheng, Guo-Zhi Wen, Chao Fang, Cheng-Bo Duan, Bo Wang. 2014-12-17. Global quantum discord in infinite quantum spin chains. https://arxiv.org/abs/1412.5285

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