Renormalized parameters and perturbation theory in dynamical mean-field theory for the Hubbard model

摘要

We calculate the renormalized parameters for the quasiparticles and their interactions for the Hubbard model in the paramagnetic phase as deduced from the low-energy Fermi-liquid fixed point using the results of a numerical renormalization-group calculation (NRG) and dynamical mean-field theory (DMFT). Even in the low-density limit there is significant renormalization of the local quasiparticle interaction U, in agreement with estimates based on the two-particle scattering theory of J. Kanamori [Prog. Theor. Phys. 30,275 (1963)]. On the approach to the Mott transition we find a finite ratio for U/D, where 2D is the renormalized bandwidth, which is independent of whether the transition is approached by increasing the on-site interaction U or on increasing the density to half filling. The leading ω~2 term in the self-energy and the local dynamical spin and charge susceptibilities are calculated within the renormalized perturbation theory (RPT) and compared with the results calculated directly from the NRG-DMFT. We also suggest, more generally from the DMFT, how an approximate expression for the q,ω spin susceptibility χ(q,ω) can be derived from repeated quasiparticle scattering with a local renormalized scattering vertex.