Valence bond entanglement entropy of frustrated spin chains

TL;DR

This paper extends the valence bond entanglement entropy to general SU(2) wave functions, enabling numerical analysis of frustrated spin chains and their quantum phase transitions, with insights into bipartition dependence.

Contribution

It introduces a reformulation allowing computation of valence bond entanglement entropy for arbitrary SU(2) wave functions in frustrated spin systems.

Findings

Locates quantum phase transition via entropy scaling

Compares valence bond and von Neumann entropy scalings

Highlights bipartition dependence of valence bond entropy

Abstract

We extend the definition of the recently introduced valence bond entanglement entropy to arbitrary SU(2) wave functions of S=1/2 spin systems. Thanks to a reformulation of this entanglement measure in terms of a projection, we are able to compute it with various numerical techniques for frustrated spin models. We provide extensive numerical data for the one-dimensional J1-J2 spin chain where we are able to locate the quantum phase transition by using the scaling of this entropy with the block size. We also systematically compare with the scaling of the von Neumann entanglement entropy. We finally underline that the valence-bond entropy definition does depend on the choice of bipartition so that, for frustrated models, a "good" bipartition should be chosen, for instance according to the Marshall sign.