Spinon and bound state excitation "light cones" in Heisenberg XXZ Chains

TL;DR

This paper studies the out-of-equilibrium dynamics in Heisenberg XXZ chains after a local quench, revealing that bound states can propagate faster than spinons, affecting information transfer and equilibration.

Contribution

It demonstrates that spin-wave bound states can dominate the light-cone velocity in XXZ chains near the isotropic point, a novel insight into excitation dynamics.

Findings

Bound states propagate faster than spinons near the isotropic point.

Light-cone velocity is determined by bound states in certain regimes.

System approaches equilibrium with induced magnetization near the interface.

Abstract

We investigate the out-of-equilibrium dynamics after a local quench that connects two spin-1/2 XXZ chains prepared in the ground state of the Hamiltonian in different phases, one in the ferromagnetic phase and the other in the critical phase. We analyze the time evolution of the on-site magnetization and bipartite entanglement entropy via adaptive time-dependent density matrix renormalization group. In systems with short-range inter- actions, such as the one we consider, the velocity of information transfer is expected to be bounded, giving rise to a light-cone effect. Interestingly, our results show that, when the anisotropy parameter of the critical chain is sufficiently close to that of the isotropic ferromagnet, the light cone is determined by the velocity of spin-wave bound states that propagate faster than single-particle ("spinon") excitations. Furthermore, we investigate how the system approaches equilibrium in the inhomogeneous ground state of the connected system, in which the ferromagnetic chain induces a nonzero magnetization in the critical chain in the vicinity of the interface.