Entanglement spreading after local fermionic excitations in the XXZ chain

TL;DR

This paper investigates how entanglement spreads after local fermionic excitations in the XXZ chain, using numerical and theoretical methods to understand quasiparticle contributions and effects of different initial states.

Contribution

It introduces a quasiparticle ansatz for entanglement spreading in the XXZ chain, accounting for various excitations and initial states, validated by DMRG and conformal field theory.

Findings

The ansatz accurately predicts entropy profiles in the gapless phase for moderate anisotropy.

Local Majorana fermion excitation causes a nontrivial rescaling of entropy profiles.

Different excitations, like domain walls, require modified quasiparticle models.

Abstract

We study the spreading of entanglement produced by the time evolution of a local fermionic excitation created above the ground state of the XXZ chain. The resulting entropy profiles are investigated via density-matrix renormalization group calculations, and compared to a quasiparticle ansatz. In particular, we assume that the entanglement is dominantly carried by spinon excitations traveling at different velocities, and the entropy profile is reproduced by a probabilistic expression involving the density fraction of the spinons reaching the subsystem. The ansatz works well in the gapless phase for moderate values of the XXZ anisotropy, eventually deteriorating as other types of quasiparticle excitations gain spectral weight. Furthermore, if the initial state is excited by a local Majorana fermion, we observe a nontrivial rescaling of the entropy profiles. This effect is further investigated in a conformal field theory framework, carrying out calculations for the Luttinger liquid theory. Finally, we also consider excitations creating an antiferromagnetic domain wall in the gapped phase of the chain, and find again a modified quasiparticle ansatz with a multiplicative factor.