Eur. Phys. J. B (2013) 86: 279
https://doi.org/10.1140/epjb/e2013-40340-8

Regular Article

Bell-CHSH function approach to quantum phase transitions in matrix product systems

¹ School of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan 430000, P.R. China
² Department of Physics, Beijing Normal University, Beijing 100875, P.R. China

^a e-mail: sunzhaoyu2012@gmail.com

Received: 22 February 2013
Received in final form: 12 April 2013
Published online: 19 June 2013

Abstract

Recently, nonlocality and Bell inequalities have been used to investigate quantum phase transitions (QPTs) in low-dimensional quantum systems. Nonlocality can be detected by the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) function. In this work, we extend the study of the Bell-CHSH function (BCF) to QPTs in matrix product systems (MPSs). In these kinds of QPTs, the ground-state energy remains analytical in the vicinity of the QPT points, and they are usually called MPS-QPTs. For several typical models, our results show that the BCF can signal MPS-QPTs very well. In addition, we find the BCF can capture signal of QPTs in unentangled states and classical states, for which other measures of quantum correlation (quantum entanglement and quantum discord) fail. Furthermore, we find that in these MPSs, there exists some kind of quantum correlation which cannot be characterized by entanglement, or by nonlocality.