Cumulant expansion for systems with large spins

TL;DR

This paper introduces a cumulant expansion method for large spin systems, providing a systematic way to derive temperature-dependent quantum corrections to classical Hamiltonians, applicable to models like the Heisenberg Hamiltonian.

Contribution

It develops a cumulant-based expansion technique using coherent states to approximate thermodynamic functions of large spin systems with quantum corrections.

Findings

Effective classical Hamiltonian with quantum corrections derived

Method applicable to Heisenberg and similar spin models

Allows classical solution techniques for quantum spin systems

Abstract

A method is proposed for obtaining a systematic expansion of thermodynamic functions of spin systems with large spin S in powers of 1/S. It uses the cumulant technique and a coherent-state representation of the partition function Z. The expansion of Z in terms of cumulants yields an effective classical Hamiltonian with temperature-dependent quantum corrections. For the Heisenberg quantum Hamiltonian, they have a non-Heisenberg form. The effective Hamiltonian can be solved by methods familiar for classical systems.