Geometric entanglement in a one-dimensional valence-bond solid state

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 Affleck-Kennedy-Lieb-Tasaki 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 an 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.