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理论物理通讯：英文版

The Antiferromagnetic Correlations in the Half—Filled Double—Exchange Model at Finite Temperature

JIAn-Chun, WANGJing

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

We extend a previous result of ours [G.S. Tian, Phys. Rev. B63 (2001) 224413] on the antiferromagneticspin correlations in the half-filled Hubbard model at finite temperature to the double-exchange model. To overcome themathematical difficulty caused by the S = 3/2 localized spin freedom in this model, we apply both Zener's argumentand the finite-temperature spin-reflection-positivity method to show rigorously that, at any temperature T, the spincorrelations in the half-filled double-exchange model are predominantly antiferromagnetic. This conclusion is completelyconsistent with the experimental observations and the previous theoretical results by approximate methods.

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We extend a previous result of ours [G.S. Tian, Phys. Rev. B63 (2001) 224413] on the antiferromagnetic spin correlations in the half-filled Hubbard model at finite temperature to the double-exchange model. To overcome the mathematical difficulty caused by the localized spin freedom in this model, we apply both Zener's argument and the finite-temperature spin-reflection-positivity method to show rigorously that, at any temperature , the spin correlations in the half-filled double-exchange model are predominantly antiferromagnetic. This conclusion is completely consistent with the experimental observations and the previous theoretical results by approximate methods.
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With the aim of contributing to a better understanding of the finite-temperature properties of low-dimensional strongly correlated systems we study a one-dimensional half-filled-band extended Hubbard model with a term of exchange interaction between neighboring sites. We analyze the temperature dependence of the specific heat, internal energy, entropy, number of doubly occupied sites, magnetic susceptibility, spin-spin correlation functions, and also investigate a detailed diagram of magnetic correlations. We use the method of small-cluster exact diagonalization calculations with the application of the grand canonical ensemble and of extrapolation techniques to the infinite chain. Our results show that the examined model exhibits a rich structure of magnetic properties due to the competition between the onsite Coulombian repulsion and the exchange interaction.
The exchange-correlation potential formalism previously introduced and applied to the one-dimensional Hubbard model has been extended to spin systems and applied to the case of the one-dimensional antiferromagnetic spin-12\frac{1}{2}21​ Heisenberg model. Within the spin exchange-correlation potential formulation, a sum rule for spin systems is derived. The exchange-correlation potential for the Heisenberg model is extrapolated from exact diagonalization results of small antiferromagnetic Heisenberg clusters. This procedure is also employed to revisit and computationally improve the previous investigation of the exchange-correlation potential of the half-filled Hubbard model, which was based on the exchange-correlation potential of the dimer. Numerical comparisons with exact benchmark calculations for both the Heisenberg and the Hubbard models indicate that, starting from the exchange-correlation potential of a finite cluster, the extrapolation procedure yields a one-particle spectral function with favorable accuracy at a relatively low computational cost. In addition, a comparison between the ground-state energies for the one-dimensional Hubbard and Heisenberg models displays how the well-known similarity in behavior of the two models at large interactions manifests itself within the exchange-correlation potential formalism.
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