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.
Highlights
Spin liquids are exotic phases of matter where the competition between strong antiferromagnetic interactions and geometric frustration prevents magnetic ordering, but instead gives rise to topological order, that is, a global ordering in the structure of their entanglement, and which display a range of exotic properties such as fractional excitations with exotic statistics [1,2,3]
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 wave functions to a trimer and SU(3) setting. We demonstrate that these models carry a Z3 symmetry which originates in the structure of trimers and the SU(3) representation theory, and which becomes the only symmetry under renormalization
A combination of analytical reasoning and numerical analysis reveals that the quantum order displayed by the model depends on the relative weight assigned to different types of trimers—it can display either Z3 topological order or form a symmetry-broken trimer crystal, and in addition possesses a point with an enhanced U(1) symmetry and critical behavior
Summary
Spin liquids are exotic phases of matter where the competition between strong antiferromagnetic interactions and geometric frustration prevents magnetic ordering, but instead gives rise to topological order, that is, a global ordering in the structure of their entanglement, and which display a range of exotic properties such as fractional excitations with exotic statistics [1,2,3]. [19], an SU(3) spin liquid on the kagome lattice had been proposed whose “orthogonal” version is an RG fixed point, namely the Z3 loop gas version of the toric code, and which was shown to be topological While this model itself did not allow for an interpretation as a superposition of trimer patterns, a modification of the SU(3) model which gave rise to such an interpretation was discussed, and numerically found to be in a trivial phase. Our construction allows us to obtain a simple SU(3) spin liquid ansatz on the kagome lattice which has a natural interpretation as a resonating singlet pattern and as a superposition of simple product states which are connected through local moves It highlights the importance of a new aspect in trimer models, and more generally N-mer models, as opposed to dimer models, namely, the key role played by the relative weights assigned to different trimer configurations. The section closes with a brief discussion of the SU(3) model as a variational ansatz
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