Quantum entanglement and quantum phase transition for the Ising model on a two-dimension square lattice

Yu-Liang Xu, Xiang-Mu Kong, Zhong-Qiang Liu and Chun-Yang Wang

Physica A: Statistical Mechanics and its Applications, 2016, vol. 446, issue C, 217-223

Abstract: The quantum entanglement and quantum phase transition of the transverse-field Ising model on a two-dimensional square lattice were investigated by applying the quantum renormalization group method. The quantum critical point (QCP) and the correlation length exponent, ν, were obtained. By taking the concurrence as a measure of entanglement, the entanglement between spin blocks near the QCP is calculated as the size of the system becomes large. The entanglement reaches a maximum close to QCP, and can exist in a small range around QCP just at the limit of thermodynamics. The nonanalytic behavior of the derivative of the entanglement with the external field shows that the system undergoes a second order quantum phase transition from a ferromagnetic phase to a paramagnetic phase. The finite-size scaling behavior of the entanglement is described, and the relationship between the entanglement exponent, θ, the correlation length exponent, ν, and the dimension of the system d is also found, i.e., θ=1/(νd).

Keywords: Quantum entanglement; Quantum phase transition; Spin system; Renormalization group (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:446:y:2016:i:c:p:217-223

DOI: 10.1016/j.physa.2015.12.002

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