Possible uniform-flux chiral spin liquid states in the SU(3) ring-exchange model on the triangular lattice

TL;DR

This paper explores possible uniform-flux chiral spin liquid states in an SU(3) ring-exchange model on a triangular lattice, revealing competing ordered and chiral spin liquid phases with distinct topological properties.

Contribution

It introduces a slave-fermion mean field approach to identify and analyze chiral spin liquid states with specific flux patterns and topological Chern numbers in the SU(3) ring-exchange model.

Findings

Identified two three-sublattice-ordered states: antiferro-quadrupolar and 120° antiferromagnetic.

Discovered gapped uniform c/3-flux and 2c/3-flux chiral spin liquids with Chern numbers +1 and +2.

Provided effective Chern-Simons theories for the chiral spin liquids.

Abstract

We consider a SU(3) model with antiferromagnetic three-site ring exchanges, in addition to two-site exchanges, on the triangular lattice. We first present numerical site-factorized state studies on the magnetic ordered states, which shows two different three-sublattice-ordered states, the antiferro-quadrupolar phase and the standard 120^o anti-ferromagnetic phase, along the axis of the strength of the three-site ring exchanges. We further study the model using slave-fermion mean field approaches in which we rewrite the exchange operators in terms of three flavors of fermions. At the mean-field level, we find the main competing trial states are the trimer state (triangular plaquette state), gapped uniform \pi/3-flux chiral spin liquid, and gapped uniform 2\pi/3-flux chiral spin liquid. The filled band of the \pi/3-flux chiral spin liquid has Chern number +1, and that of the 2\pi/3-flux chiral spin liquid has Chern number +2. We also give the effective Chern-Simons theory for each chiral spin liquid at the mean-field level.