Singlet ground states of the bilinear-biquadratic exchange Hamiltonian with reflection symmetry

Abstract

We apply the Lieb–Schupp method to the isotropic spin-S Hamiltonian with bilinear (−J/S2) and biquadratic (−J′/S4) exchange interactions on finite lattices with reflection-symmetry to prove that finite volume ground states of the models are spin singlet in the parameter region J′ ≥ 2S2J, J′ ≥ 0.