Linked-cluster series-expansion technique for quantum spin systems

Abstract

The linked-cluster series expansion is developed for use on models of quantum spin systems with single-ion potentials. A Wick-like theorem is used to calculate the \ensuremath{\tau} integrals occurring in the series expansion. Such a new approach can deal with many realistic models of magnetic materials and will yield high-accuracy results in both ordered and disordered phases. These developments are illustrated by calculating the first seven terms of the linked-cluster series for the free energy, susceptibility, specific heat, and spontaneous magnetization of the spin-1 anisotropic Heisenberg model with a uniaxial single-ion potential. Thermodynamic properties of the system in both paramagnetic and magnetically ordered phases are discussed including the magnetization and susceptibility as functions of temperature, the critical exponents \ensuremath{\beta} and \ensuremath{\gamma}, and the existence of tricritical and bicritical points.