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

TL;DR

This paper calculates renormalized parameters for quasiparticles in the Hubbard model using NRG-DMFT, revealing significant interaction renormalization and properties near the Mott transition, and compares perturbation theory with direct calculations.

Contribution

It introduces a method to compute renormalized parameters and interactions in the Hubbard model within DMFT, providing insights into quasiparticle behavior near the Mott transition.

Findings

Significant renormalization of local quasiparticle interaction $ ilde U$ even at low densities.

Finite ratio of $ ilde U/ ilde D$ near the Mott transition, independent of transition approach.

Agreement between renormalized perturbation theory and direct NRG-DMFT calculations.

Abstract

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 $\tilde U$, in agreement with estimates based on the two-particle scattering theory of Kanamori (1963). On the approach to the Mott transition we find a finite ratio for $\tilde U/\tilde D$, where $2\tilde D$ 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 $\omega^2$ 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. The dynamic ${\bf q},\omega$ spin susceptibility $\chi({\bf q},\omega)$ is also estimated from repeated quasiparticle scattering with a local renormalized scattering vertex.