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arXiv · 1708.00848

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

Olivier Gauthé·Didier Poilblanc
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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 ${\bf 94}$, 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.

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Olivier Gauthé, Didier Poilblanc. 2017-09-19. Entanglement properties of the two-dimensional SU(3) AKLT state. https://doi.org/10.1103/physrevb.96.121115

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