Entanglement Entropy of One-dimensional Gapped Spin Chains

TL;DR

This paper studies the entanglement entropy in one-dimensional gapped spin chains, revealing how boundary edge states significantly influence EE and how different models affect residual entanglement.

Contribution

It demonstrates the role of boundary effective spins in EE for both S=1/2 and S=1 gapped chains, and compares the effects of model deformations on entanglement.

Findings

Edge states contribute significantly to EE in gapped chains.

Localized boundary spins explain EE in S=1/2 chains.

Deforming the model reduces residual entanglement in S=1 chains.

Abstract

We investigate the entanglement entropy (EE) of gapped S=1 and $S=1/2$ spin chains with dimerization. We find that the effective boundary degrees of freedom as edge states contribute significantly to the EE. For the $S=1/2$ dimerized Heisenberg chain, the EE of the sufficiently long chain is essentially explained by the localized $S=1/2$ effective spins on the boundaries. As for S=1, the effective spins are also $S=1/2$ causing a Kennedy triplet that yields a lower bound for the EE. In this case, the residual entanglement reduces substantially by a continuous deformation of the Heisenberg model to that of the AKLT Hamiltonian.