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Fermi Liquid Behavior in the 2D Hubbard Model at Low Temperatures

Abstract.

We prove that the weak coupling 2D Hubbard model away from half filling is a Landau Fermi liquid up to exponentially small temperatures. In particular we show that the wave function renormalization is an order 1 constant and essentially temperature independent in the considered range of temperatures and that the interacting Fermi surface is a regular convex curve. This result is obtained by deriving a convergent expansion (which is not a power series) for the two point Schwinger function by Renormalization Group methods and proving at each order suitable power counting improvements due to the convexity of the interacting Fermi surface. Convergence follows from determinant bounds for the fermionic expectations.

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Correspondence to G. Benfatto.

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Communicated by Vincent Rivasseau

Submitted: January 4, 2006 Accepted: January 31, 2006

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Benfatto, G., Giuliani, A. & Mastropietro, V. Fermi Liquid Behavior in the 2D Hubbard Model at Low Temperatures. Ann. Henri Poincaré 7, 809–898 (2006). https://doi.org/10.1007/s00023-006-0270-z

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Keywords

  • Span Tree
  • Fermi Surface
  • Hubbard Model
  • Wave Function Renormalization
  • Trivial Vertex