A computational method for exchange-coupled systems

Abstract

A computer procedure is developed to generate matrix solutions of quantum-mechanical problems given only the appropriate Hamiltonian. The method is considered with particular reference to the solution of the Heisenberg exchange Hamiltonian. The solution of the crystal field, spin-orbit coupling, and magnetic field Hamiltonians is also discussed. The magnetic and thermodynamic properties of several types of finite one-dimensional exchange-coupled systems are calculated within the spin-only formalism, with the properties of the corresponding infinite systems being obtained by extrapolation. The significance of the intercluster coupling parameter θ is determined by comparison with these exact calculations. Extension of the computational technique to exchange between orbitally degenerate ions is discussed.