The eigenstates of short chains of spin-1 atoms with Heisenberg and biquadratic exchange

Abstract

The eigenstates of chains of up to eight spin-1 atoms interacting with both Heisenberg and biquadratic exchange are calculated numerically. The ground state is found to be ferromagnetic or antiferromagnetic for most values of the exchange but can be anomalous for certain ranges. An extension of Munro's exact results is also presented, which involves an assumption about the ground state of a system with biquadratic exchange only.