Original Paper

Annales Henri Poincaré

, Volume 7, Issue 5, pp 809-898

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

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

  • G. BenfattoAffiliated withMathematics Department, University of Rome “Tor Vergata” Email author 
  • , A. GiulianiAffiliated withPhysics Department, Princeton University
  • , V. MastropietroAffiliated withMathematics Department, University of Rome “Tor Vergata”


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.