Entanglement evolution across defects in critical anisotropic Heisenberg chains

TL;DR

This paper investigates how local defects affect entanglement dynamics in anisotropic Heisenberg chains after a quench, revealing that defect relevance depends on the sign of bulk interactions and influences entanglement saturation.

Contribution

It provides a detailed analysis of out-of-equilibrium entanglement evolution in anisotropic Heisenberg chains with defects, highlighting the role of interaction sign in defect relevance.

Findings

For attractive interactions, defects are irrelevant and entanglement evolution matches defect-free case.

For repulsive interactions, defects are relevant and cause entanglement saturation.

The results extend known ground-state entanglement properties to out-of-equilibrium dynamics.

Abstract

We study the out-of-equilibrium time evolution after a local quench connecting two anisotropic spin-1/2 XXZ Heisenberg open chains via an impurity bond. The dynamics is obtained by means of the adaptive time-dependent density-matrix renormalization group. We show that the entanglement entropies (Von Neumann and R\'enyi), in the presence of a weakened bond depend on the sign of the bulk interaction. For attractive interaction (\Delta< 0), the defect turns out to be irrelevant and the evolution is asymptotically equivalent to the one without defect obtained by conformal field theory. For repulsive interaction (\Delta>0), the defect is relevant and the entanglement saturates to a finite value. This out-of-equilibrium behavior generalizes the well known results for the ground-state entanglement entropy of the model.