Quench Dynamics of Topological Maximally-Entangled States

TL;DR

This paper studies the dynamics of topological entangled states in quantum chains after a quench, revealing how their evolution depends on a pseudo magnetic field and identifying conditions for their stability and decay.

Contribution

It introduces a framework linking the evolution of entangled edge states to a time-dependent pseudo magnetic field and characterizes their stability through winding numbers and Berry phases.

Findings

Maximally-entangled edge states depend on the winding of the pseudo magnetic field.

Stable edge states require nontrivial Berry phases.

Edge states decay over a timescale proportional to system size.

Abstract

We investigate the quench dynamics of the one-particle entanglement spectra (OPES) for systems with topologically nontrivial phases. By using dimerized chains as an example, it is demonstrated that the evolution of OPES for the quenched bi-partite systems is governed by an effective Hamiltonian which is characterized by a pseudo spin in a time-dependent pseudo magnetic field $\vec{S}(k,t)$. The existence and evolution of the topological maximally-entangled edge states are determined by the winding number of $\vec{S}(k,t)$ in the $k$-space. In particular, the maximally-entangled edge states survive only if nontrivial Berry phases are induced by the winding of $\vec{S}(k,t)$. In the infinite time limit the equilibrium OPES can be determined by an effective time-independent pseudo magnetic field $\vec{S}_{\mb{eff}}(k)$. Furthermore, when maximally-entangled edge states are unstable, they are destroyed by quasiparticles within a characteristic timescale in proportional to the system size.