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Physical review. B, Condensed matter

Magnetic excitation in the Hubbard-Hirsch model

Xiangdong Zhang, Bo‐Zang Li, Fu‐Cho Pu

Published Jul 1, 1996• 1 citation
Publisher

Abstract

Based on the Hubbard-Hirsch model, we studied the dynamical susceptibility and spin excitation of an itinerant-electron system within the random-phase approximation by using a Green's-function technique. It is shown that the two-center matrix elements in the Hubbard-Hirsch model not only change the dynamic property of the susceptibility, but also widen the gap between two spin subbands, which suppresses the electron-hole single excitations. In contrast, the region of collective excitations of the spin becomes larger. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.54.44

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Based on the Hubbard-Hirsch model, we studied the dynamical susceptibility and spin excitation of an itinerant-electron system within the random-phase approximation by using a Green's-function technique. It is shown that the two-center matrix elements in the Hubbard-Hirsch model not only change the dynamic property of the susceptibility, but also widen the gap between two spin subbands, which suppresses the electron-hole single excitations. In contrast, the region of collective excitations of the spin becomes larger. \textcopyright{} 1996 The American Physical Society.
Investigation have been carried out on the spin wave energy of a ferromagnet using the random-phase approximation (RPA) in the Stoner model. Based on the Hubbard-Hirsch Hamiltonian, in this paper we study the spin excitation in an itinerant-electron system with the Hartree-Fock Approximation (HFA) to derive the analytic expressions of the dynamical susceptibility of the spin system, by setting up the equation of motion and solving it in a generalized HFA of the susceptibility tensor, Χ-+, and quoting the result for the first derivative of the Green's function. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 579-582
Dynamic spin susceptibility is calculated for the t-J model in the paramagnetic phase by applying the memory function method in terms of the Hubbard operators. A self-consistent system of equations for the memory function is obtained within the mode coupling approximation. Both itinerant hole excitations and localized spin fluctuations give contributions to the memory function. Spin dynamics have a diffusive character in the hydrodynamic limit; spin-wave-like excitations are regained in the high-frequency region.
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We investigate the spin and charge susceptibilities of the two-dimensional Hubbard model based upon the perturbative calculation in the strength of correlation U. For U comparable to a bare bandwidth, the charge susceptibility decreases near half filling as hole doping approaches zero. This behavior suggesting the precursor of the Mott-Hubbard gap formation cannot be obtained without the vertex corrections beyond the random-phase approximation. In the low-temperature region, the spin susceptibility deviates from the Curie-Weiss-like law and finally turns to decrease with the decrease of temperature. This spin-gap-like behavior originates from the van Hove singularity in the density of states. \textcopyright{} 1996 The American Physical Society.
The Hubbard model is used as a starting point for a study of an electronic system with spin ½. Using a functional integral representation at half-filling it is demonstrated that the spin degeneracy is equivalent to dynamic Ising spins coupled to the fermions. A magnetic phase transition of the model is related to a transition of the Ising spins from a paramagnetic to an antiferromagnetic phase. A metal-insulator transition in the paramagnetic phase can be described within this approach by the Green's function of non-interacting fermions, coupled to Ising spins. This picture is compared with the earlier Ising spin representation of the Hubbard model by Hirsch and discussed in terms of a small hopping amplitude.