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arXiv:0705.3818 · Physical Review B

Field-dependent quasiparticles in a strongly correlated local system. II.

Johannes Bauer, Alex C. Hewson

Published Jul 25, 2007• 19 citations
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Abstract

We extend the renormalized quasiparticle description of the symmetric Anderson model in a magnetic field $H$, developed in earlier work, to the nonsymmetric model. The renormalized parameters are deduced from the low energy numerical renormalization group (NRG) fixed point for arbitrary field values. We find quasiparticle resonance widths, ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}}_{\ensuremath{\sigma}}(H)$, which depend in general on the spin $\ensuremath{\sigma}$ as well as $H$. The low temperature static properties can be expressed completely in terms of these parameters, which can also be used as inputs for a renormalized perturbation theory. We show that taking into account repeated quasiparticle scattering gives results for the longitudinal and transverse dynamic spin susceptibilities which are in very good agreement with those obtained from direct NRG calculations.

DOI
10.1103/physrevb.76.035119

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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 UUU. The low energy results are analyzed in terms of quasiparticles with field-dependent parameters. These 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, ${z}_{\ensuremath{\sigma}}(H)$, differ according to the spin type $\ensuremath{\sigma}=\ensuremath{\uparrow}$ or $\ensuremath{\sigma}=\ensuremath{\downarrow}$. 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.
We show that the functional renormalization group is a numerically cheap method to obtain the low-energy behavior of the Anderson impurity model describing a localized impurity level coupled to a bath of conduction electrons. Our approach uses an external magnetic field as the flow parameter, partial bosonization of the transverse spin fluctuations, and frequency-independent interaction vertices determined by Ward identities. The magnetic field serves also as a regulator for the bosonized spin fluctuations, which are suppressed at large field. We calculate the quasiparticle residue and spin susceptibility in the particle-hole symmetric case and obtain excellent agreement with the Bethe ansatz results for arbitrary coupling.
The unusual low temperature behaviour of metals and metal alloys, such as heavy fermion systems, Mott insulators and unconventional superconductors, has been a central topic of scientific investigation for over half a century. Due to strong correlations between the many particles, the solution to most theoretical models of these systems is difficult because standard perturbation methods break down. In certain cases, non-perturbative renormalization group approaches can be used to access the low energy behaviour and take into account the effects of strong correlations. However, these methods do not work for several important and interesting classes of model. These include lattice models with finite dimension, models with impurities of high degeneracy and steady state transport through quantum dots. The aim of this thesis is therefore to develop a new and general renormalization group approach that will lend itself to wide application in models where existing techniques fail. The method explored here utilises renormalized perturbation theory (RPT) in conjunction with scaling equations and collective excitations. It is tested on the single impurity Anderson model, the paradigmatic model used to understand magnetic impurities within a non-magnetic host metal. The Anderson model is simple yet exhibits interesting features due to strong correlation, such as a single renormalized low energy scale called the Kondo temperature. This model is also well understood as it has been solved using the numerical renormalization group (NRG), which provides ample numerical data against which this new technique is compared. Finally, a preliminary study is given for this method when it is applied to a wider class of models.
We calculate the spin and charge dynamical susceptibilities of a strongly correlated impurity model in a renormalised perturbation theory. The irreducible for vertices for the quasiparticle scattering are deduced from the renormalised parameters, which have been calculated by fitting of the low-lying levels of a numerical renormalisation group (NRG) calculation to those of an effective Anderson model. The susceptibilities are asymptotically exact in the low frequency limit and satisfy the Korringa-Shiba relation. By comparing the results with those calculated from a direct NRG calculation, we show that the renormalised perturbation theory (RPT) description gives a very good description of spin dynamics for all values of the local interaction U, not only at low frequencies but over the whole relevant frequency range. In the presence of a magnetic field the approach can be generalised using field dependent renormalised parameters to calculate the transverse and parallel spin dynamic susceptibilities. The RPT results give accurate results for the spin dynamics over the whole frequency range and for all values of the magnetic field.