Fermi surface renormalization in Hubbard ladders

Abstract

We derive the one-loop renormalization equations for the shift in the Fermi wave vectors for one-dimensional interacting models with four Fermi points (two left and two right movers) and two Fermi velocities ${v}_{1}$ and ${v}_{2}.$ We find the shift to be proportional to ${(v}_{1}\ensuremath{-}{v}_{2}{)U}^{2},$ where U is the Hubbard U. Our results apply to the Hubbard ladder and to the ${t}_{1}\ensuremath{-}{t}_{2}$ Hubbard model. The Fermi sea with fewer particles tends to empty. The stability of a saddle point due to shifts of the Fermi energy and the shift of the Fermi wave vector at the Mott-Hubbard transition are discussed.