The two dimensional Hubbard Model at half-filling: I. Convergent Contributions

Vincent Rivasseau

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arXiv · cond-mat/0107118

The two dimensional Hubbard Model at half-filling: I. Convergent Contributions

Vincent Rivasseau

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Abstract

We prove analyticity theorems in the coupling constant for the Hubbard model at half-filling. The model in a single renormalization group slice of index $i$ is proved to be analytic in $λ$ for $|λ| \le c/i$ for some constant $c$, and the skeleton part of the model at temperature $T$ (the sum of all graphs without two point insertions) is proved to be analytic in $λ$ for $|λ| \le c/|\log T|^{2}$. These theorems are necessary steps towards proving that the Hubbard model at half-filling is {\it not} a Fermi liquid (in the mathematically precise sense of Salmhofer).

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Vincent Rivasseau. 2001-07-05. The two dimensional Hubbard Model at half-filling: I. Convergent Contributions. https://arxiv.org/abs/cond-mat/0107118

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