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New Solutions of the T-Matrix Theory of the Attractive Hubbard Model

K. S. D. Beach·R. J. Gooding·F. Marsiglio
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Abstract

This short paper summarizes a calculational method for obtaining the dynamical properties of many-body theories formulated in terms of (unrenormalized) bare propagators (and more generally, in terms of meromorphic functions, or convolutions over meromorphic functions) to a very high accuracy. We demonstrate the method by applying it to a T-matrix theory of the attractive Hubbard model in two dimensions. We expand the pair propagator using a partial fraction decomposition, and then solve for the residues and pole locations of such a decomposition using a computer algebra system to an arbitrarily high accuracy (we used MapleV and obtained these quantities to a relative error of 10^(-80)). Thus, this method allows us to bypass all inaccuracies associated with the traditional analytical continuation problem. Our results for the density of states make clear the pronounced development of a pseudogap as the temperature is lowered in this formulation of the attractive Hubbard model.

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K. S. D. Beach, R. J. Gooding, F. Marsiglio. 1999-12-10. New Solutions of the T-Matrix Theory of the Attractive Hubbard Model. https://doi.org/10.1016/s0921-4534(00)00724-3

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