Exact Results for the Bipartite Entanglement Entropy of the AKLT spin-1 chain

TL;DR

This paper provides exact analytical results for the entanglement entropy of the AKLT spin-1 chain with open boundaries, revealing how it approaches specific constants related to the system's degeneracy and correlation length.

Contribution

It presents new exact formulas for the entanglement entropy of all four degenerate ground states of the AKLT chain, extending previous known results.

Findings

Entanglement entropy approaches ln(2) and 2ln(2) for different ground states.

The approach to the asymptotic values is exponential with a correlation length of 1/ln(3).

Provides exact analytical results for all degenerate ground states.

Abstract

We study the entanglement between two domains of a spin-1 AKLT chain subject to open boundary conditions. In this case the ground-state manifold is four-fold degenerate. We summarize known results and present additional exact analytical results for the von Neumann entanglement entropy, as a function of both the size of the domains and the total system size for {\it all} four degenerate ground-states. In the large $l,L$ limit the entanglement entropy approaches $\ln(2)$ and $2\ln(2)$ for the $S^z_T=\pm 1$ and $S^z_T=0$ states, respectively. In all cases, it is found that this constant is approached exponentially fast defining a length scale $\xi=1/\ln(3)$ equal to the known bulk correlation length.