TY - JOUR

T1 - Entanglement entropy of a three-spin-interacting spin chain with a time-reversal-breaking impurity at one boundary

AU - Nag, Tanay

AU - Rajak, Atanu

N1 - Publisher Copyright:
© 2018 American Physical Society.

PY - 2018/4/9

Y1 - 2018/4/9

N2 - We investigate the effect of a time-reversal-breaking impurity term (of strength λd) on both the equilibrium and nonequilibrium critical properties of entanglement entropy (EE) in a three-spin-interacting transverse Ising model, which can be mapped to a p-wave superconducting chain with next-nearest-neighbor hopping and interaction. Importantly, we find that the logarithmic scaling of the EE with block size remains unaffected by the application of the impurity term, although, the coefficient (i.e., central charge) varies logarithmically with the impurity strength for a lower range of λd and eventually saturates with an exponential damping factor [∼exp(-λd)] for the phase boundaries shared with the phase containing two Majorana edge modes. On the other hand, it receives a linear correction in term of λd for an another phase boundary. Finally, we focus to study the effect of the impurity in the time evolution of the EE for the critical quenching case where the impurity term is applied only to the final Hamiltonian. Interestingly, it has been shown that for all the phase boundaries, contrary to the equilibrium case, the saturation value of the EE increases logarithmically with the strength of impurity in a certain regime of λd and finally, for higher values of λd, it increases very slowly dictated by an exponential damping factor. The impurity-induced behavior of EE might bear some deep underlying connection to thermalization.

AB - We investigate the effect of a time-reversal-breaking impurity term (of strength λd) on both the equilibrium and nonequilibrium critical properties of entanglement entropy (EE) in a three-spin-interacting transverse Ising model, which can be mapped to a p-wave superconducting chain with next-nearest-neighbor hopping and interaction. Importantly, we find that the logarithmic scaling of the EE with block size remains unaffected by the application of the impurity term, although, the coefficient (i.e., central charge) varies logarithmically with the impurity strength for a lower range of λd and eventually saturates with an exponential damping factor [∼exp(-λd)] for the phase boundaries shared with the phase containing two Majorana edge modes. On the other hand, it receives a linear correction in term of λd for an another phase boundary. Finally, we focus to study the effect of the impurity in the time evolution of the EE for the critical quenching case where the impurity term is applied only to the final Hamiltonian. Interestingly, it has been shown that for all the phase boundaries, contrary to the equilibrium case, the saturation value of the EE increases logarithmically with the strength of impurity in a certain regime of λd and finally, for higher values of λd, it increases very slowly dictated by an exponential damping factor. The impurity-induced behavior of EE might bear some deep underlying connection to thermalization.

UR - http://www.scopus.com/inward/record.url?scp=85045383695&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.97.042108

DO - 10.1103/PhysRevE.97.042108

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C2 - 29758713

AN - SCOPUS:85045383695

SN - 2470-0045

VL - 97

JO - Physical Review E

JF - Physical Review E

IS - 4

M1 - 042108

ER -