Effective field theory for the SO(n) bilinear-biquadratic spin chain

TL;DR

This paper develops a low-energy effective field theory for the SO(n) bilinear-biquadratic spin chain using Majorana fermions, characterizing phases and relating theories for different n, with implications for entanglement and correlation functions.

Contribution

It introduces a novel effective field theory approach for SO(n) spin chains, generalizing known results and proposing a reduction mechanism for understanding ground states.

Findings

Characterized phases of SO(6) spin chain

Established relations between SO(6) and SO(5) theories

Proposed a reduction mechanism for arbitrary SO(n)

Abstract

We present a low-energy effective field theory to describe the SO(n) bilinear-biquadratic spin chain. We start with n=6 and construct the effective theory by using six Majorana fermions. After determining various correlation functions we characterize the phases and establish the relation between the effective theories for SO(6) and SO(5). Together with the known results for n=3 and 4, a reduction mechanism is proposed to understand the ground state for arbitrary SO(n). Also, we provide a generalization of the Lieb-Schultz-Mattis theorem for SO(n). The implications of our results for entanglement and correlation functions are discussed.