Entanglement of quantum spin systems: a valence-bond approach

TL;DR

This paper reviews various methods for quantifying entanglement in quantum spin systems, focusing on valence-bond basis estimators, and presents new results on entanglement in spin 1 chains.

Contribution

It clarifies the connections between geometric entanglement estimators and observables, and provides new insights into spin 1 chain entanglement properties.

Findings

Comparison of entanglement estimators in valence-bond basis

New results on entanglement in spin 1 chains

Clarification of geometric and observable connections

Abstract

In order to quantify entanglement between two parts of a quantum system, one of the most used estimator is the Von Neumann entropy. Unfortunately, computing this quantity for large interacting quantum spin systems remains an open issue. Faced with this difficulty, other estimators have been proposed to measure entanglement efficiently, mostly by using simulations in the valence-bond basis. We review the different proposals and try to clarify the connections between their geometric definitions and proper observables. We illustrate this analysis with new results of entanglement properties of spin 1 chains.