Entanglement properties of the two-dimensional SU(3) AKLT state

Abstract

Two-dimensional (spin-$2$) Affleck-Kennedy-Lieb-Tasaki (AKLT) type valence bond solids on the square lattice are known to be symmetry protected topological (SPT) gapped spin liquids [Shintaro Takayoshi, Pierre Pujol, and Akihiro Tanaka Phys. Rev. B $94$, 235159 (2016)]. Using the projected entangled pair state (PEPS) framework, we extend the construction of the AKLT state to the case of $SU(3)$, relevant for cold atom systems. The entanglement spectrum is shown to be described by an alternating $SU(3)$ chain of "quarks" and "antiquarks", subject to exponentially decaying (with distance) Heisenberg interactions, in close similarity with its $SU(2)$ analog. We discuss the SPT feature of the state.

arXiv comment6 pages, 5 figures. v3: added one figure and more details. Accepted for PRB rapid com

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• Locality at the boundary implies gap in the bulk for 2D PEPS
• Quantum spin liquid phases in the bilinear-biquadratic two-SU(4)-fermion Hamiltonian on the square lattice
• SU(4) topological RVB spin liquid on the square lattice