Magnetic Field Behaviour of a Haldane Gap Antiferromagnet

TL;DR

This paper studies how magnetic fields affect a Haldane gap antiferromagnet, using exact diagonalization and perturbation theory to analyze level crossings and experimental implications.

Contribution

It provides a detailed analysis of magnetic field effects on a Haldane gap system with general anisotropy, including exact diagonalization and symmetry explanations.

Findings

Splitting of the Haldane triplet as a function of magnetic field.

Identification of level crossings due to discrete symmetries.

Relevance to ESR and neutron scattering experiments on NENP.

Abstract

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).