Survival probability in a quenched Majorana chain with an impurity

Quench dynamics of edge states in a finite extended Su-Schrieffer-Heeger system

We examine the quench dynamics of an extended Su-Schrieffer-Heeger (SSH) model involving long-range hopping that can hold multiple topological phases. Using winding number diagrams to characterize the system's topological phases geometrically, it is shown that there can be multiple winding number transition paths for a quench between two topological phases. The dependence of the quench dynamics is studied in terms of the survival probability of the fermionic edge modes and postquench transport. For two quench paths between two topological regimes with the same initial and final topological phase, the survival probability of edge states is shown to be strongly dependent on the winding number transition path. This dependence is explained using energy band diagrams corresponding to the paths. Following this, the effect of the winding number transition path on transport is investigated. We find that the velocities of maximum transport channels varied along the winding number transition path. This variation depends on the path we choose, i.e., it increases or decreases depending upon the path. An analysis of the coefficient maps, energy spectrum, and spatial structure of the edge states of the final quench Hamiltonian provides an understanding of the path-dependent velocity variation phenomenon.

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

We investigate the effect of a time-reversal-breaking impurity term (of strength λ_{d}) 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 λ_{d} and eventually saturates with an exponential damping factor [∼exp(-λ_{d})] 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 λ_{d} 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 λ_{d} and finally, for higher values of λ_{d}, it increases very slowly dictated by an exponential damping factor. The impurity-induced behavior of EE might bear some deep underlying connection to thermalization.