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We study the spreading of entanglement produced by the time evolution of alocal fermionic excitation created above the ground state of the XXZ chain. Theresulting entropy profiles are investigated via density-matrix renormalizationgroup calculations, and compared to a quasiparticle ansatz. In particular, weassume that the entanglement is dominantly carried by spinon excitationstraveling at different velocities, and the entropy profile is reproduced by aprobabilistic expression involving the density fraction of the spinons reachingthe subsystem. The ansatz works well in the gapless phase for moderate valuesof the XXZ anisotropy, eventually deteriorating as other types of quasiparticleexcitations gain spectral weight. Furthermore, if the initial state is excitedby a local Majorana fermion, we observe a nontrivial rescaling of the entropyprofiles. This effect is further investigated in a conformal field theoryframework, carrying out calculations for the Luttinger liquid theory. Finally,we also consider excitations creating an antiferromagnetic domain wall in thegapped phase of the chain, and find again a modified quasiparticle ansatz witha multiplicative factor.

Entanglement spreading after local fermionic excitations in the XXZ chain