2 research outputs found
Renormalization group analysis of the 2D Hubbard model
Salmhofer [Commun. Math. Phys. 194, 249 (1998)] has recently developed a new
renormalization group method for interacting Fermi systems, where the complete
flow from the bare action of a microscopic model to the effective low-energy
action, as a function of a continuously decreasing infrared cutoff, is given by
a differential flow equation which is local in the flow parameter. We apply
this approach to the repulsive two-dimensional Hubbard model with nearest and
next-nearest neighbor hopping amplitudes. The flow equation for the effective
interaction is evaluated numerically on 1-loop level. The effective
interactions diverge at a finite energy scale which is exponentially small for
small bare interactions. To analyze the nature of the instabilities signalled
by the diverging interactions we extend Salmhofers renormalization group for
the calculation of susceptibilities. We compute the singlet superconducting
susceptibilities for various pairing symmetries and also charge and spin
density susceptibilities. Depending on the choice of the model parameters
(hopping amplitudes, interaction strength and band-filling) we find
commensurate and incommensurate antiferromagnetic instabilities or d-wave
superconductivity as leading instability. We present the resulting phase
diagram in the vicinity of half-filling and also results for the density
dependence of the critical energy scale.Comment: 16 pages, RevTeX, 16 eps figure