Quantum entanglement and quantum phase transitions in frustrated Majumdar–Ghosh model

Abstract

By using the density matrix renormalization group technique, the quantum phase transitions in the frustrated Majumdar–Ghosh model are investigated. The behaviors of the conventional order parameter and the quantum entanglement entropy are analyzed in detail. The order parameter is found to peak at J 2 ∼ 0.58 , but not at the Majumdar–Ghosh point ( J 2=0.5). Although, the quantum entanglements calculated with different subsystems display dissimilarly, the extremes of their first derivatives approach to the same critical point. By finite size scaling, this quantum critical point J C 2 converges to around 0.301 in the thermodynamic limit, which is consistent with those predicted previously by some authors (Tonegawa and Harada, 1987 [6]; Kuboki and Fukuyama, 1987 [7]; Chitra et al., 1995 [9]). Across the J C 2, the system undergoes a quantum phase transition from a gapless spin-fluid phase to a gapped dimerized phase.