Entanglement dynamics after quenches with inhomogeneous Hamiltonians

TL;DR

This paper derives analytical formulas for entanglement dynamics in inhomogeneous quantum chains, revealing how inhomogeneity suppresses transport and entanglement growth, with extensions to interacting systems showing similar qualitative behavior.

Contribution

It provides a detailed analytical framework for entanglement evolution in inhomogeneous Hamiltonians, including scattering effects and extensions to interacting chains.

Findings

Strong inhomogeneity suppresses entanglement growth and transport.

Analytical formulas match numerical simulations in non-interacting models.

Entanglement can increase even when transport is suppressed, at intermediate times.

Abstract

We investigate entanglement dynamics in bipartite systems governed by inhomogeneous Hamiltonians of the form $H = H_L + H_R$, where $H_{L/R}$ acts only on the left or right region and is homogeneous within each region. Focusing on the XX chain and the transverse-field Ising chain, we derive analytical formulas for the entanglement entropy between the two regions in the hydrodynamic limit of long times. In this regime, fermions incident on the interface undergo scattering, generating entanglement between reflected and transmitted modes. The resulting quasiparticle picture is controlled by the transmission coefficient, which we obtain analytically by solving the stationary lattice Schr\"odinger equation. Due to the bounded dispersion, strong inhomogeneity suppresses both transport and entanglement growth. We benchmark our analytical predictions against numerical simulations in paradigmatic setups. Finally, we extend the analysis to the interacting XXZ chain using tDMRG. The numerical data show qualitative agreement with the quadratic case: entanglement growth remains suppressed in the strongly inhomogeneous limit. Notably, however, entanglement continues to increase even when transport is suppressed, at least at intermediate times.