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

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.

5 pages. Accepted version

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Cited by in corpus (12)

• SU$(3{)}_1$ Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS
• Variational methods for contracting projected entangled-pair states
• A class of two-dimensional AKLT models with a gap
• Phase diagram of the chiral SU(3) antiferromagnet on the kagome lattice
• Quantum spin liquid phases in the bilinear-biquadratic two-SU(4)-fermion Hamiltonian on the square lattice
• Quantum trimer models and topological SU(3) spin liquids on the kagome lattice
• SU(4) topological RVB spin liquid on the square lattice
• Classification of symmetry-enriched topological quantum spin liquids
• Exact hole-induced $SU(N)$ flavor-singlets in certain $U=\infty$ $SU(N)$ Hubbard models
• Entanglement spectra of non-chiral topological (2+1)-dimensional phases with strong time-reversal breaking, Li-Haldane state counting, and PEPS
• Entanglement Spectrum as a diagnostic of chirality of Topological Spin Liquids: Analysis of an $\mathrm{SU}(3)$ PEPS
• Matrix Product Wave Function of the Ground State and Elementary Excitation in the Spin-1/2 Chain