Global quantum discord and matrix product density operators

Hai-Lin Huang, Hong-Guang Cheng, Xiao Guo, Duo Zhang, Yuyin Wu, Jian Xu and Zhao-Yu Sun ()
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Hai-Lin Huang: School of Electrical and Electronic Engineering, Wuhan Polytechnic University
Hong-Guang Cheng: School of Electrical and Electronic Engineering, Wuhan Polytechnic University
Xiao Guo: School of Electrical and Electronic Engineering, Wuhan Polytechnic University
Duo Zhang: School of Electrical and Electronic Engineering, Wuhan Polytechnic University
Yuyin Wu: School of Electrical and Electronic Engineering, Wuhan Polytechnic University
Jian Xu: School of Electrical and Electronic Engineering, Wuhan Polytechnic University
Zhao-Yu Sun: School of Electrical and Electronic Engineering, Wuhan Polytechnic University

The European Physical Journal B: Condensed Matter and Complex Systems, 2018, vol. 91, issue 6, 1-9

Abstract: 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 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1140/epjb/e2018-80691-x

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