Entanglement Spectra of the 2D AKLT Model: VBS/CFT Correspondence

TL;DR

This paper explores the entanglement properties of the 2D AKLT model's VBS state, revealing a holographic spin chain correspondence and confirming area law behavior with sub-ln(2) prefactor.

Contribution

It demonstrates a novel holographic correspondence between the entanglement spectra of the 2D VBS state and a thermal spin chain, linking it to CFT predictions.

Findings

Entanglement entropy follows an area law with a sub-ln(2) prefactor.

Entanglement spectra resemble those of a holographic spin chain.

Comparison with CFT supports the holographic spin chain model.

Abstract

We investigate the entanglement properties of the valence-bond-solid (VBS) state defined on two-dimensional lattices, which is the exact ground state of the Affleck-Kennedy-Lieb-Tasaki model. It is shown that the entanglement entropy obeys an area law and the non-universal prefactor of the leading term is strictly less than $\ln 2$. The analysis of entanglement spectra for various lattices reveals that the reduced density matrix associated with the VBS state is closely related to a thermal density matrix of a {\it holographic} spin chain, whose spectrum is reminiscent of that of the spin-1/2 Heisenberg chain. This correspondence is further supported by comparing the entanglement entropy in the holographic spin chain with conformal field theory predictions.