Magnetic Field Behaviour of a Haldane Gap Antiferromagnet

We investigate the magnetic field behaviour of an antiferromagnetic Heisenberg spin-1 chain with the most general single-ion anisotropy. We discuss the regime in which the magnetic field is below the transition value. The splitting of the Haldane triplet is obtained as a function of a field applied in an arbitrary orientation by means of a Lancz\H os exact diagonalization of chains of up to 16 spins. Our results are nicely summarized in terms of a first-order perturbation theory. We explain various level crossings that occur by the existence of discrete symmetries. A discussion is given of the electron spin resonance and neutron scattering experiments on the compound Ni(C$_2$H$_8$N$_2$)$_2$NO$_2$ClO$_4$ (NENP).