Universal front propagation in the quantum Ising chain with domain-wall initial states

TL;DR

This paper demonstrates a universal behavior in the propagation of domain walls in the quantum Ising chain, linking noncritical and critical cases, and explores how different initial excitations influence magnetization profiles and entanglement entropy.

Contribution

It reveals a universal magnetization profile in the ferromagnetic phase of the Ising chain for certain initial states and extends the understanding of domain-wall melting in quantum spin chains.

Findings

Universal magnetization profiles for local initial excitations

Loss of universality for non-local domain-wall excitations

Entanglement entropy saturates at ground-state value

Abstract

We study the melting of domain walls in the ferromagnetic phase of the transverse Ising chain, created by flipping the order-parameter spins along one-half of the chain. If the initial state is excited by a local operator in terms of Jordan-Wigner fermions, the resulting longitudinal magnetization profiles have a universal character. Namely, after proper rescalings, the profiles in the noncritical Ising chain become identical to those obtained for a critical free-fermion chain starting from a step-like initial state. The relation holds exactly in the entire ferromagnetic phase of the Ising chain and can even be extended to the zero-field XY model by a duality argument. In contrast, for domain-wall excitations that are highly non-local in the fermionic variables, the universality of the magnetization profiles is lost. Nevertheless, for both cases we observe that the entanglement entropy asymptotically saturates at the ground-state value, suggesting a simple form of the steady state.