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

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 $\mathbf{q},\omega$ spin susceptibility $\chi (\mathbf{q},\omega )$ is also estimated from repeated quasiparticle scattering with a local renormalized scattering vertex.

arXiv comment13 pages 19 figures

References in corpus (26)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• The numerical renormalization group method for quantum impurity systems
• Heavy Fermions and Quantum Phase Transitions
• How do Fermi liquids get heavy and die?
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Scattering and Pairing in Cuprate Superconductors
• Non-perturbative many-body approach to the Hubbard model and single-particle pseudogap
• Zero temperature metal-insulator transition in the infinite-dimensional Hubbard model
• Cluster Dynamical Mean Field Theory of the Mott Transition
• The one-dimensional Hubbard model: A reminiscence
• Renormalized Parameters for Impurity Models
• Impact of nonlocal correlations over different energy scales: A Dynamical Vertex Approximation study
• Magnetic Field Effects on Quasiparticles in Strongly Correlated Local Systems
• Competition between antiferromagnetic and charge order in the Hubbard-Holstein model
• Spectral properties of the three-dimensional Hubbard model
• Extremely correlated Fermi liquid theory meets Dynamical mean-field theory: Analytical insights into the doping-driven Mott transition
• Field dependent quasiparticles in the infinite dimensional Hubbard model
• Field dependent quasiparticles in models of strongly correlated electrons
• Mott insulators and the doping-induced Mott transition within DMFT: exact results for the one-band Hubbard model
• Quasiparticle properties of strongly correlated electron systems with itinerant metamagnetic behavior
• Low energy physics of the t-J model in $d=\infty$ using Extremely Correlated Fermi Liquid theory: Cutoff Second Order Equations
• Phase diagram and critical points of a double quantum dot
• Convergence of energy scales on the approach to a local quantum critical point
• Renormalized quasiparticles in antiferromagnetic states of the Hubbard model
• Effect of pairing fluctuations on the spin resonance in Fe-based superconductors
• High-order terms in the renormalized perturbation theory for the Anderson impurity model

Cited by in corpus (3)

• Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory
• Fermi Liquids and the Luttinger Integral
• Magnetic field-dependent dynamics and field-driven metal-to-insulator transition of the half-filled Hubbard model: A DMFT+DMRG study