Fermi liquid behavior in the 2D Hubbard model at low temperatures

TL;DR

This paper proves that the weak coupling 2D Hubbard model away from half filling exhibits Fermi liquid behavior at low temperatures, with stable Fermi surface and constant wave function renormalization, using Renormalization Group techniques.

Contribution

It establishes Fermi liquid behavior in the 2D Hubbard model at low temperatures through a convergent expansion and Renormalization Group analysis, a significant theoretical advancement.

Findings

Wave function renormalization remains order 1 and temperature independent.

Interacting Fermi surface is a regular convex curve.

Fermi liquid behavior holds up to exponentially small 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.