Entanglement Entropy and Quantum Phase Transition in the O(N) σ-model

Gargi Das, Aritra Ghosh, Bhabani Prasad Mandal

Li-Tuo Shen, Xuan-Tong Pei, Zhi‐Cheng Shi +1 more

Jiunn-Wei Chen, Shou-Huang Dai, Jin-Yi Pang

Abstract We investigate how entanglement entropy behaves in a non-conformal scalar field system with a quantum phase transition, by the replica method. We study the σ-model in 3+1 dimensions which is O(N) symmetric as the mass squared parameter μ2 is positive, and undergoes spontaneous symmetry breaking while μ2 becomes negative. The area law leading divergence of the entanglement entropy is preserved in both of the symmetric and the broken phases. The spontaneous symmetry breaking changes the subleading divergence from log to log squared, due to the cubic interaction on the cone. At the leading order of the coupling constant expansion, the entanglement entropy reaches a cusped maximum at the quantum phase transition point μ2 = 0, and decreases while μ2 is tuned away from 0 into either phase.

Anonymous, Tangi Morvan, Irénée Frérot +1 more

Tobias J. Osborne

Chunjian Zhao, Zhiguo Lü, Hang Zheng

The ground state and the spectral structure of lower-lying excited states of a dissipative two-level system coupled to a sub-Ohmic bath (s = 1/2) with nonzero bias have been studied using the unitary transformation method. By calculating the ground-state entanglement entropy, the ground-state average of σ(z)(G), and the static susceptibility of the two-level system, we explore the nature of the transition (crossover) between the delocalized and localized state of the two-level system. Furthermore, we calculate the time-dependent expectation (σ(z)(t)) and the time evolution of the entanglement entropy to show that, when the system undergoes a transition (crossover) from the delocalized to the localized state, the time evolution of the two-level system changes from coherent to decoherent dynamics.