A gapped SU(3) spin liquid with Z_3 topological order

TL;DR

This paper constructs a gapped SU(3) symmetric topological spin liquid on the kagome lattice, demonstrating its equivalence to a Z_3 quantum double model and revealing chiral entanglement properties.

Contribution

It introduces a novel SU(3) symmetric topological spin liquid model using PEPS and proves its local equivalence to a Z_3 quantum double model, with insights into its entanglement spectrum.

Findings

The model is a gapped topological spin liquid with Z_3 order.

Numerical analysis shows no phase transition or long-range order.

Entanglement spectrum exhibits chiral features consistent with SU(3)_1 CFT.

Abstract

We construct a topological spin liquid (TSL) model on the kagome lattice, with SU(3) symmetry with the fundamental representation at each lattice site, based on Projected Entangled Pair States (PEPS). Using the PEPS framework, we can adiabatically connect the model to a fixed point model (analogous to the dimer model for Resonating Valence Bond states) which we prove to be locally equivalent to a $Z_3$ quantum double model. Numerical study of the interpolation reveals no sign of a phase transition or long-range order, characterizing the model conclusively as a gapped TSL. We further study the entanglement spectrum of the model and find that while it is gapped, it exhibits branches with vastly different velocities, with the slow branch matching the counting of a chiral $SU(3)_1$ CFT, suggesting that it can be deformed to a model with chiral $SU(3)_1$ entanglement spectrum.