Entanglement dynamics of Majorana fermions in one dimension

We study the ground-state phase diagram and dynamics of one-dimensional Kitaev model of spinless p-wave superconductor with several competing interactions. We first map out the ground-state phase diagram of the model and characterize the phases by the edge modes, the correlation functions, and the entanglement spectrum. We then investigate the dynamical properties during interaction sweeps across the critical point using the time-dependent Bogoliubov theory. When the sweep speed is slow compared to the typical time scale at the critical point, both correlation function and entanglement entropy exhibit spatially periodic structures after the system passes the critical interaction strength. On top of this, we find that the degeneracy structure of the entanglement spectrum changes in time during the sweep. [1] By explicitly calculating the above quantities for excited states, we attribute these behaviors to the Bogoliubov quasiparticles excited near the critical points. We also show that the entanglement spectrum reflects the pattern of the Majorana correlation for the excited states.
[1] T. Ohta, S. Tanaka, I. Danshita, and K. Totsuka, Phys. Rev. B 93, 165423 (2016).