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

A. C. Hewson
Phys. Rev. B 94, 195152 – Published 28 November 2016

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 Ũ, 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 Ũ/D̃, where 2D̃ 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 ω2 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.

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  • Received 9 August 2016
  • Revised 14 November 2016

DOI:https://doi.org/10.1103/PhysRevB.94.195152

©2016 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. C. Hewson

  • Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom

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Issue

Vol. 94, Iss. 19 — 15 November 2016

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