Looking at the Haldane Conjecture from a Grouptheoretical Point of View

TL;DR

This paper investigates the Haldane Conjecture through a group-theoretical approach, analyzing degeneracies in spin Hamiltonians with different symmetries and perturbations.

Contribution

It introduces a five-parameter family of Spin-1 Hamiltonians with degenerate ground states based on the Lieb-Schultz-Mattis construction and explores symmetry perturbations.

Findings

Identification of Hamiltonians with degenerate ground states

Analysis of symmetry perturbations preserving degeneracy

Extension to spin-3/2 $SU(4)$ case

Abstract

Based on the Lieb-Schultz-Mattis construction we present a five parameter family of Spin-1 Hamiltonians with degenerate groundstate. Starting from the critical $SU(3)$ symmetric Hamiltonian, we look for those perturbations of the $SU(3)$ symmetry, which leave the groundstate degenerate. We also discuss the spin-3/2 $SU(4)$-case.