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arXiv:cond-mat/9708009 · International Journal of Modern Physics B

The Hubbard Model in the Two-Pole Approximation

Adolfo Avella, Francesco Paolo Mancini, D. Villani, L. Siurakshina, V. Yu. Yushankhaï

Published Jan 10, 1998• 47 citations
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Abstract

The two-dimensional Hubbard model is analyzed in the framework of the two-pole expansion. It is demonstrated that several theoretical approaches, when considered at their lowest level, are all equivalent and share the property of satisfying the conservation of the first four spectral momenta. It emerges that the various methods differ only in the way of fixing the internal parameters and that it exists a unique way to preserve simultaneously the Pauli principle and the particle–hole symmetry. A comprehensive comparison with respect to some general symmetry properties and the data from quantum Monte Carlo analysis shows the relevance of imposing the Pauli principle.

DOI
10.1142/s0217979298000065

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The two-dimensional Hubbard model is analyzed in the framework of the two-pole expansion. It is demonstrated that several theoretical approaches, when considered at their lowest level, are all equivalent and share the property of satisfying the conservation of the first four spectral momenta. It emerges that the various methods differ only in the way of fixing the internal parameters and that it exists a unique way to preserve simultaneously the Pauli principle and the particle–hole symmetry. A comprehensive comparison with respect to some general symmetry properties and the data from quantum Monte Carlo analysis shows the relevance of imposing the Pauli principle.
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The charge and spin dynamics of the two-dimensional Hubbard model in the paramagnetic phase is first studied by means of the two-pole approximation within the framework of the composite operator method. The fully self-consistent scheme requires: no decoupling, the fulfillment of both Pauli principle and hydrodynamic constraints, the simultaneous solution of fermionic and bosonic sectors, and a very rich momentum dependence of the response functions. The temperature and momentum dependencies, as well as the dependency on the Coulomb repulsion strength and the filling, of the calculated charge and spin susceptibilities and correlation functions are in very good agreement with the numerical calculations present in the literature.
Using a Green's-function equation of motion approach the two-dimensional Hubbard model is studied. The decoupling of the hierarchy is performed according to the conserving of the first four spectral moments. Beyond the Roth's two-pole approximation, the damping effect occurs naturally. The energy dispersions at various fillings, the spectral weight, and the density of states are calculated. Comparisons with the quantum Monte Carlo results and the cluster perturbation theory show that our approach can capture some essential features of the Hubbard model.
Using a Green's-function equation of motion approach the two-dimensional Hubbard model is studied. The decoupling of the hierarchy is performed according to the conserving of the first four spectral moments. Beyond the Roth's two-pole approximation, the damping effect occurs naturally. The energy dispersions at various fillings, the spectral weight, and the density of states are calculated. Comparisons with the quantum Monte Carlo results and the cluster perturbation theory show that our approach can capture some essential features of the Hubbard model.
We calculate the single-particle spectral function for the Hubbard model within the framework of a projection technique equivalent to the two-pole approximation. We show that the two-pole approximation can be well understood as an average characterization of the upper and the lower Hubbard bands, rather than describing a dispersive quasiparticle. By comparing with numerical spectra of finite Hubbard rings and of a 4\ifmmode\times\else\texttimes\fi{}4 cluster [P. W. Leung et al., Phys. Rev. B 46, 11 779 (1992)], we show that the present approximation is capable of reproducing essential properties of the single-particle spectral function. In particular, the two-pole spectrum is characterized by a direct gap, in agreement with the exact spectrum. We emphasize the role of local antiferromagnetic correlations.