Entanglement spreading after local and extended excitations in a free-fermion chain

TL;DR

This paper investigates how entanglement evolves over time in a free-fermion chain after local and extended excitations, revealing distinct entropy behaviors depending on the type and arrangement of excitations.

Contribution

It provides a detailed analysis of entanglement dynamics for various excitations, highlighting differences in coherence preservation and entropy scaling in a free-fermion system.

Findings

Single particle/hole excitation yields a single excess entropy unit at large times.

Double holes preserve some coherence, with entropy additive at large separations.

Extended holes show logarithmic entropy scaling, while separated holes show linear scaling.

Abstract

We study the time evolution of entanglement created by local or extended excitations upon the ground state of a free-fermion chain. A single particle or hole excitation produces a single bit of excess entropy for large times and subsystem lengths. In case of a double hole, some of the coherence between the excitations is preserved and the excess entropy becomes additive only for large hole separations. In contrast, the coherence is always lost for particle-hole excitations. Multiple hole excitations on a completely filled chain are also investigated. We find that for an extended contiguous hole the excess entropy scales logarithmically with the size, whereas the increase is linear for finite separations between the holes.