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Physical review. B, Solid state

High-Spin Expansion for Heisenberg Spin Systems

Michael E. Harrigan, Gerald L. Jones

Published Jun 1, 1973• 10 citations
Publisher

Abstract

It is known that in a well-defined high-spin limit, the properties of systems of quantum spins approach those of a corresponding system of classical spins. In this paper we give a method for computing corrections to this limit. We give the first nontrivial corrections to the partition function and spin-spin correlation function for a linear chain of Heisenberg-coupled spins. We briefly discuss possible comparisons with experiment.

DOI
10.1103/physrevb.7.4897

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It is known that in a well-defined high-spin limit, the properties of systems of quantum spins approach those of a corresponding system of classical spins. In this paper we give a method for computing corrections to this limit. We give the first nontrivial corrections to the partition function and spin-spin correlation function for a linear chain of Heisenberg-coupled spins. We briefly discuss possible comparisons with experiment.
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 . The expansion of 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.
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.
(received; accepted) PACS. 05.30.-d – Quantum statistical mechanics. PACS. 75.10.Jm – Quantized spin models. PACS. 75.10.Hk – Classical spin models. Abstract. – A method for obtaining a systematic expansion of thermodynamic functions of spin systems with large spin S in powers of 1/S is proposed. This method 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. In recent years considerable interest in condensed matter physics has been focusing on the properties of new magnetic materials, such as magnetic molecules with a large effective spin S, or intermetallic compounds containing magnetic layers or chains. For the latter, most of the theoretical studies deal with S = 1/2 systems which, in the one-dimensional case, allow for analytical solutions using special methods such as the Bethe Ansatz or Jordan-Wigner
A simple Monte Carlo high-temperature expansion method to evaluate the partition function of quantum spin systems which was proposed in the previous paper l) is improved so that all of the needed expansion-coefficients are obtained from interpolating points of less than ten with an interpolation formula. By this improvement, this method is applicable to the finite spin-systems of rather large spin size regardless of dimensionality of the system. As an example, the method is applied to the one-dimensional spin-l/2 isotropic Heisenberg ferromagnetic system.