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.

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

References in corpus (13)

• Many-Body Physics with Ultracold Gases
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Ultracold Gases of Ytterbium: Ferromagnetism and Mott States in an SU(6) Fermi System
• Spin-orbital quantum liquid on the honeycomb lattice
• Resonating valence bond states in the PEPS formalism
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Exact Diagonalization of Heisenberg SU(N) models
• Exact results for SU(3) spin chains: trimer states, valence bond solids, and their parent Hamiltonians
• Z_3 symmetry-protected topological phases in the SU(3) AKLT model
• SU(N) quantum spin models: A variational wavefunction study
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• Infinite Matrix Product States for long range SU(N) spin models
• Field theory of symmetry-protected valence bond solid states in (2+1) dimensions

Cited by in corpus (2)

• Phase diagram of the chiral SU(3) antiferromagnet on the kagome lattice
• SU(4) topological RVB spin liquid on the square lattice