Domain-wall melting and entanglement in free-fermion chains with a band structure

TL;DR

This paper investigates how a domain wall melts in free-fermion chains with band structures, revealing logarithmic entanglement growth proportional to the number of filled bands and universal entropy features.

Contribution

It demonstrates the impact of band structure on domain-wall melting and entanglement dynamics in free-fermion chains, including a rescaling effect in dimerized systems.

Findings

Entanglement grows logarithmically with time, scaled by the number of filled bands.

Particle density and current resemble homogeneous cases with velocity rescaling.

Universal entropy contribution doubles in dimerized chains.

Abstract

We study the melting of a domain wall in free-fermion chains, where the periodic variation of the hopping amplitudes gives rise to a band structure. It is shown that the entanglement grows logarithmically in time, and the prefactor is proportional to the number of filled bands in the initial state. For a dimerized chain the particle density and current are found to have the same expressions as in the homogeneous case, up to a rescaling of the velocity. The universal contribution to the entropy profile is then doubled, while the non-universal part can be extracted numerically from block-Toeplitz matrices.