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

2001/07/05 by Vincent Rivasseau, Rivasseau, Vincent
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Physics of Superconductivity and Magnetism #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el) #Theoretical and Computational Physics #cond-mat.str-el #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.cond-mat/0107118

31 pages, 2 figures

arxiv created 2001/07/05 · openalex publication_date 2001/07/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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| ≤ 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| ≤ 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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