Geometric Entanglement in a One-Dimensional Valence Bond Solid State

TL;DR

This paper analytically calculates the geometric entanglement in the AKLT chain, showing it saturates quickly to a constant for large blocks, marking a first for gapped 1D systems far from criticality.

Contribution

It provides the first analytical derivation of geometric entanglement in a gapped 1D quantum many-body system.

Findings

Geometric entanglement saturates exponentially for large block sizes.

First analytical calculation of geometric entanglement in a gapped 1D system.

Results applicable far from quantum critical points.

Abstract

In this paper we provide the analytical derivation of the global geometric entanglement per block for the valence bond solid ground state of the spin-1 AKLT chain. In particular, we show that this quantity saturates exponentially fast to a constant when the sizes of the blocks are sufficiently large. Our result provides the first known example of an analytical calculation of the geometric entanglement for a gapped quantum many-body system in one dimension and far away from a quantum critical point.