Quasiclassical Hamiltonians for large-spin systems

TL;DR

This paper introduces a method to derive effective classical Hamiltonians for large-spin quantum systems using coherent states and cumulant expansion, enabling classical analysis of complex quantum spin models.

Contribution

It presents a novel approach to obtain non-Heisenberg effective Hamiltonians for large-spin systems, incorporating quantum corrections in a form suitable for classical methods.

Findings

Effective Hamiltonians include non-Heisenberg many-spin terms.

Method applicable to Heisenberg-type quantum Hamiltonians.

Potential explanation for phenomena like spin-Peierls transition.

Abstract

We propose a method for obtaining effective classical Hamiltonians \cal H for many-body quantum spin systems with large spins. This method uses the coherent-state representation of the partition function Z and the cumulant expansion in powers of 1/S. For the quantum Hamiltonian \hat H of a Heisenberg form, the 1/S corrections in \cal H have a non-Heisenberg many-spin form. The effective Hamiltonian \cal H can be treated by methods familiar for classical systems. The non-Heisenberg terms in \cal H may be responsible for such effects as spin-Peierls transition and uplifting of the classical degeneracy by quantum fluctuations.