Relaxation of the entanglement spectrum in quench dynamics of topological systems

In this paper, we investigate how the entanglement spectrum relaxes to its steady-state values in one-dimensional quadratic systems after a quantum quench. In particular, we apply saddle-point expansion to dimerized chains and 1D p-wave superconductors. We found the entanglement spectrum to always exhibit a power-law relaxation superimposed with oscillations at certain characteristic angular frequencies. For dimerized chains, we found the exponent ν of the power-law decay to always be $3/2$. For 1D p-wave superconductors, however, we found that, depending on the initial and final Hamiltonian, the exponent ν can take its value from a limited list of values, the smallest possible of which is $\nu =1/2$, which leads to a very slow convergence to its steady-state value. (paper: quantum statistical physics, condensed matter, integrable systems)