Valence Bond Entanglement Entropy

TL;DR

This paper introduces the Valence Bond Entanglement Entropy for SU(2) quantum spin systems, demonstrating its effectiveness in capturing entanglement features across various dimensions and phases using Quantum Monte Carlo methods.

Contribution

It defines a new entanglement measure based on valence bonds and shows its numerical equivalence to von Neumann entropy in 1D systems, extending to 2D models.

Findings

Valence Bond Entanglement Entropy matches von Neumann entropy in 1D systems.

Area law observed for Valence Bond Solid states in 2D.

Logarithmic corrections found in the Neel phase of 2D models.

Abstract

We introduce for SU(2) quantum spin systems the Valence Bond Entanglement Entropy as a counting of valence bond spin singlets shared by two subsystems. For a large class of antiferromagnetic systems, it can be calculated in all dimensions with Quantum Monte Carlo simulations in the valence bond basis. We show numerically that this quantity displays all features of the von Neumann entanglement entropy for several one-dimensional systems. For two-dimensional Heisenberg models, we find a strict area law for a Valence Bond Solid state and multiplicative logarithmic corrections for the Neel phase.