2014/12/17 by Zhao-Yu Sun, Zhao‐Yu Sun, Yan-E Liao +25
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Quantum many-body systems #quant-ph
paper · pdf · doi:10.48550/arxiv.1412.5285
arxiv created 2014/12/17 · openalex publication_date 2014/12/17 · arxiv updated 2014/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.