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Global quantum discord and matrix product density operators

  • Hai-Lin Huang
  • Hong-Guang Cheng
  • Xiao Guo
  • Duo Zhang
  • Yuyin Wu
  • Jian Xu
  • Zhao-Yu Sun
Regular Article
  • 3 Downloads

Abstract

In a previous study, we have proposed a procedure to study global quantum discord in 1D chains whose ground states are described by matrix product states [Z.-Y. Sun et al., Ann. Phys. 359, 115 (2015)]. In this paper, we show that with a very simple generalization, the procedure can be used to investigate quantum mixed states described by matrix product density operators, such as quantum chains at finite temperatures and 1D subchains in high-dimensional lattices. As an example, we study the global discord in the ground state of a 2D transverse-field Ising lattice, and pay our attention to the scaling behavior of global discord in 1D sub-chains of the lattice. We find that, for any strength of the magnetic field, global discord always shows a linear scaling behavior as the increase of the length of the sub-chains. In addition, global discord and the so-called “discord density” can be used to indicate the quantum phase transition in the model. Furthermore, based upon our numerical results, we make some reliable predictions about the scaling of global discord defined on the n × n sub-squares in the lattice.

Keywords

Solid State and Materials 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Hai-Lin Huang
    • 1
  • Hong-Guang Cheng
    • 1
  • Xiao Guo
    • 1
  • Duo Zhang
    • 1
  • Yuyin Wu
    • 1
  • Jian Xu
    • 1
  • Zhao-Yu Sun
    • 1
  1. 1.School of Electrical and Electronic Engineering, Wuhan Polytechnic UniversityWuhanP.R. China

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