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

TL;DR

This paper constructs and analyzes the entanglement properties of a two-dimensional SU(3) AKLT state, revealing its SPT nature and entanglement spectrum structure using PEPS framework, extending known SU(2) results.

Contribution

It introduces a novel SU(3) AKLT state on a 2D lattice and characterizes its entanglement spectrum and SPT features, expanding the understanding of topological quantum states.

Findings

Entanglement spectrum described by an alternating SU(3) chain

State exhibits symmetry protected topological (SPT) order

Entanglement interactions decay exponentially with distance

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.