Quantum trimer models and topological SU(3) spin liquids on the kagome lattice

TL;DR

This paper introduces quantum trimer models on the kagome lattice that exhibit Z_3 topological order or symmetry-breaking phases, providing new insights into SU(3) spin liquids and their potential for topological quantum computation.

Contribution

It constructs exact parent Hamiltonians for SU(3) trimer models with topological degeneracy and explores their phase diagram, including topological and symmetry-broken phases.

Findings

Models exhibit Z_3 topological order or trimer crystal phases.

Parent Hamiltonians demonstrate 9-fold ground state degeneracy.

Phase behavior depends on trimer weights, with critical points showing enhanced symmetry.

Abstract

We construct and study quantum trimer models and resonating SU(3)-singlet models on the kagome lattice, which generalize quantum dimer models and the Resonating Valence Bond wavefunctions to a trimer and SU(3) setting. We demonstrate that these models carry a Z_3 symmetry which originates in the structure of trimers and the SU(3) representation theory, and which becomes the only symmetry under renormalization. Based on this, we construct simple and exact parent Hamiltonians for the model which exhibit a topological 9-fold degenerate ground space. A combination of analytical reasoning and numerical analysis reveals that the quantum order ultimately displayed by the model depends on the relative weight assigned to different types of trimers -- it can display either Z_3 topological order or form a symmetry-broken trimer crystal, and in addition possesses a point with an enhanced U(1) symmetry and critical behavior. Our results accordingly hold for the SU(3) model, where the two natural choices for trimer weights give rise to either a topological spin liquid or a system with symmetry-broken order, respectively. Our work thus demonstrates the suitability of resonating trimer and SU(3)-singlet ansatzes to model SU(3) topological spin liquids on the kagome lattice.