Relaxation of the entanglement spectrum in quench dynamics of topological systems

TL;DR

This paper investigates how the entanglement spectrum in one-dimensional topological systems relaxes after a quantum quench, revealing power-law decay with oscillations and varying exponents depending on the system.

Contribution

It provides a detailed analysis of the relaxation dynamics of the entanglement spectrum in 1D topological systems using saddle point expansion, highlighting different decay exponents.

Findings

Entanglement spectrum exhibits power-law relaxation with oscillations.

For dimerized chains, the decay exponent is always 3/2.

For 1D p-wave superconductors, the exponent varies, with a minimum of 1/2.

Abstract

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