Field dependent quasiparticles in the infinite dimensional Hubbard model

TL;DR

This paper investigates the behavior of field-dependent quasiparticles in the infinite dimensional Hubbard model using dynamical mean field theory and numerical renormalization group, revealing spin-dependent quasiparticle weights and confirming Luttinger's theorem.

Contribution

It provides a detailed analysis of quasiparticle properties in the Hubbard model under magnetic fields, introducing two methods for determining renormalized parameters with good agreement.

Findings

Quasiparticle weights differ for spin up and down away from half-filling.

DMFT-NRG results explain local spin susceptibilities in terms of quasiparticle scattering.

Luttinger's theorem holds across all regimes and magnetic fields.

Abstract

We present dynamical mean field theory (DMFT) results for the local spectral densities of the one- and two-particle response functions for the infinite dimensional Hubbard model in a magnetic field. We look at the different regimes corresponding to half-filling, near half-filling and well away from half-filling, for intermediate and strong values of the local interaction $U$. The low energy results are analyzed in terms of quasiparticles with field dependent parameters. The renormalized parameters are determined by two different methods, both based on numerical renormalization group (NRG) calculations, and we find good agreement. Away from half-filling the quasiparticle weights, $z_\sigma(H)$, differ according to the spin type $\sigma=\uparrow$ or $\sigma=\downarrow$. Using the renormalized parameters, we show that DMFT-NRG results for the local longitudinal and transverse dynamic spin susceptibilities in an arbitrary field can be understood in terms of repeated scattering of these quasiparticles. We also check Luttinger's theorem for the Hubbard model and find it to be satisfied in all parameter regimes and for all values of the magnetic field.