Entanglement entropy dynamics of disordered quantum spin chains

TL;DR

This paper investigates how entanglement entropy evolves over time in disordered quantum spin chains after sudden parameter changes, revealing different growth behaviors depending on the final state.

Contribution

It introduces free fermionic techniques to analyze entanglement dynamics in disordered chains and explains ultraslow growth at criticality using strong disorder renormalization.

Findings

Finite entanglement entropy for non-critical states

Logarithmic double-logarithmic growth at criticality

Different behaviors for global and local quenches

Abstract

By means of free fermionic techniques we study the time evolution of the entanglement entropy, S(t), of a block of spins in the random transverse-field Ising chain after a sudden change of the parameters of the Hamiltonian. We consider global quenches, when the parameters are modified uniformly in space, as well as local quenches, when two disconnected blocks are suddenly joined together. For a non-critical final state, the dynamical entanglement entropy is found to approach a finite limiting value for both types of quenches. If the quench is performed to the critical state, the entropy grows for an infinite block as S(t) \sim ln ln t. This type of ultraslow increase is explained through the strong disorder renormalization group method.