Phase diagram of the SO(n) bilinear-biquadratic chain from many-body entanglement

TL;DR

This paper explores the phase diagram of SO(n) bilinear-biquadratic quantum spin chains using global quantum correlations, revealing known and novel phase behaviors, and proposing an infinite entanglement length at a specific point.

Contribution

It introduces a comprehensive analysis of the phase diagram for SO(n) chains via geometric entanglement, uncovering new behaviors and conjecturing their generality for all n.

Findings

Identification of known phase transitions

Discovery of novel phase diagram features

Proposal of infinite entanglement length at a biquadratic point

Abstract

Here we investigate the phase diagram of the SO(n) bilinear-biquadratic quantum spin chain by studying the global quantum correlations of the ground state. We consider the cases of n=3,4 and 5 and focus on the geometric entanglement in the thermodynamic limit. Apart from capturing all the known phase transitions, our analysis shows a number of novel distinctive behaviors in the phase diagrams which we conjecture to be general and valid for arbitrary n. In particular, we provide an intuitive argument in favor of an infinite entanglement length in the system at a purely-biquadratic point. Our results are also compared to other methods, such as fidelity diagrams.