Bulk-Edge correspondence of entanglement spectrum in 2D spin ground states

TL;DR

This paper establishes a connection between the entanglement spectrum of 2D spin ground states and the spectrum of a boundary quantum spin chain, using a quantum-to-classical mapping of Valence Bond Solid states.

Contribution

It demonstrates a bulk-edge correspondence for the entanglement spectrum in 2D spin systems via a novel quantum-to-classical mapping approach.

Findings

Entanglement spectrum corresponds to boundary spin chain spectrum.

Mapping relates 2D VBS ground states to classical O(3) models.

Boundary spectrum exhibits Heisenberg interactions.

Abstract

General local spin $S$ ground states, described by a Valence Bond Solid (VBS) on a two dimensional lattice are studied. The norm of these ground states is mapped to a classical O(3) model on the same lattice. Using this quantum-to-classical mapping we obtain the partial density matrix $\rho_{A}$ associated with a subsystem ${A}$ of the original ground state. We show that the entanglement spectrum of $\rho_{\rm A}$ in a translation invariant lattice is given by the spectrum of a quantum spin chain at the boundary of region $A$, with local Heisenberg type interactions between spin 1/2 particles.