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

• Published in: The European physical journal. B, Condensed matter physics Vol. 86; no. 6
• Main Authors: Huang, Hai-Lin, Sun, Zhao-Yu, Wang, Bo
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.06.2013; EDP Sciences; Springer
• Subjects: Complex Systems; Condensed Matter Physics; Condensed matter: electronic structure, electrical, magnetic, and optical properties; Exact sciences and technology; Fluid- and Aerodynamics; General theory and models of magnetic ordering; Magnetic properties and materials; Physics; Physics and Astronomy; Regular Article; Solid State Physics; Solid State and Materials; Quantum system; Spin ladder; Quantum entanglement; Bell inequality; Quantum phase transition; Three-body problem; Four body problem
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/e2013-40340-8

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.