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Physical review. B, Condensed matter

Critical indices in a d=1 filled-band Fermi system

Federico Bonetto, Vieri Mastropietro

Published Jul 15, 1997• 6 citations
Publisher

Abstract

By renormalization-group methods we obtain nonperturbative results about a $d=1$ system of interacting spinless fermions in a periodic potential when the conduction band is filled. Both the strength of the interaction and the amplitude of the periodic potential are assumed to be small. We determine that the large-distance asymptotic behavior of the two-point Schwinger function is anomalous and described by two critical indices, explicitly computed by convergent series, related to the renormalization of the spectral gap and of the discontinuity at the Fermi surface.

DOI
10.1103/physrevb.56.1296

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By renormalization-group methods we obtain nonperturbative results about a d=1d=1d=1 system of interacting spinless fermions in a periodic potential when the conduction band is filled. Both the strength of the interaction and the amplitude of the periodic potential are assumed to be small. We determine that the large-distance asymptotic behavior of the two-point Schwinger function is anomalous and described by two critical indices, explicitly computed by convergent series, related to the renormalization of the spectral gap and of the discontinuity at the Fermi surface.
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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.