Front dynamics in the XY chain after local excitations

TL;DR

This paper investigates the time evolution of magnetization and entanglement in the XY chain after local excitations, revealing hydrodynamic limits and interference effects, with implications for understanding quasiparticle dynamics and entropy behavior.

Contribution

It introduces a detailed analysis of local excitations in the XY chain, highlighting differences between domain walls and spin-flip excitations and their impact on hydrodynamic limits and entropy.

Findings

Hydrodynamic limit for magnetization with domain walls

Interference effects in spin-flip excitations

Entropy profile relations for different excitations

Abstract

We study the time evolution of magnetization and entanglement for initial states with local excitations, created upon the ferromagnetic ground state of the XY chain. For excitations corresponding to a single or two well separated domain walls, the magnetization profile has a simple hydrodynamic limit, which has a standard interpretation in terms of quasiparticles. In contrast, for a spin-flip we obtain an interference term, which has to do with the nonlocality of the excitation in the fermionic basis. Surprisingly, for the single domain wall the hydrodynamic limit of the entropy and magnetization profiles are found to be directly related. Furthermore, the entropy profile is additive for the double domain wall, whereas in case of the spin-flip excitation one has a nontrivial behaviour.