SU(3) trimer resonating-valence-bond state on the square lattice

TL;DR

This paper introduces an SU(3) trimer resonating-valence-bond state on the square lattice, demonstrating its gapped nature and $ ext{Z}_3$ topological order through entangled-pair state representation and topological sector analysis.

Contribution

The study constructs a novel SU(3) tRVB state with $C_{4v}$ symmetry and proves its topological order and gapped properties using entanglement and modular matrices.

Findings

Correlation functions decay exponentially, indicating a gapped state.

The state exhibits $ ext{Z}_3$ topological order.

All nine topological sectors are constructed on a torus.

Abstract

We propose and study an SU(3) trimer resonating-valence-bond (tRVB) state with $C_{4v}$ point-group symmetry on the square lattice. By devising a projected entangled-pair state representation, we show that all (connected) correlation functions between local operators in this SU(3) tRVB state decay exponentially, indicating its gapped nature. We further calculate the modular $S$ and $T$ matrices by constructing all nine topological sectors on a torus and establish the existence of $\mathbb{Z}_3$ topological order in this SU(3) tRVB state.