Exact results for SU(3) spin chains: trimer states, valence bond solids, and their parent Hamiltonians

TL;DR

This paper presents exact models for SU(3) spin chains, including a four-site interaction Hamiltonian with a three-fold degenerate ground state and valence bond solid models with different representations, analyzing their excitations and gaps.

Contribution

Introduces new exact SU(3) spin chain models, including a parent Hamiltonian for a trimer chain and valence bond solid models with specific representations, exploring their excitation spectra.

Findings

Elementary excitations transform under conjugate representation 3bar.

Only two of the valence bond solid models exhibit spinon confinement.

Some models display a Haldane gap in the excitation spectrum.

Abstract

We introduce several exact models for SU(3) spin chains: (1) a translationally invariant parent Hamiltonian involving four-site interactions for the trimer chain, with a three-fold degenerate ground state. We provide numerical evidence that the elementary excitations of this model transform under representation 3bar of SU(3) if the original spins of the model transform under rep. 3. (2) a family of parent Hamiltonians for valence bond solids of SU(3) chains with spin reps. 6, 10, and 8 on each lattice site. We argue that of these three models, only the latter two exhibit spinon confinement and a Haldane gap in the excitation spectrum.