We explore the predictions of the renormalized perturbation theory for an n-channel Anderson model, both with and without Hund's rule coupling, in the regime away from particle-hole symmetry. For the model with n=2 we deduce the renormalized parameters from numerical renormalization group calculations, and plot them as a function of the occupation at the impurity site, nd. From these we deduce the spin, orbital and charge susceptibilities, Wilson ratios and quasiparticle density of states at T=0, in the different parameter regimes, which gives a comprehensive overview of the low energy behavior of the model. We compare the difference in Kondo behaviors at the points where nd=1 and nd=2. One unexpected feature of the results is the suppression of the charge susceptibility in the strong correlation regime over the occupation number range 1 <nd <3.
The properties of current-carrying steady states of strongly correlated systems away from the linear-response regime are of topical interest. In this article, we review the renormalized perturbation theory, or renormalized SPT of reference [1] for the Anderson model. We present an extension to higher orders and compare the higher-order results with NRG calculations. Finally, we elucidate the role of Ward identities in calculating out-of-equilibrium properties and address claims made in the literature.
We demonstrate the effectiveness of a generalized renormalized perturbational approach to calculate the induced magnetization for the single impurity Anderson model with a strong on-site interaction, using flow equations for renormalized parameters to scale from a weak correlation to a strong correlation regime. We show that, using simple approximation schemes in different parameter regimes, remarkably accurate results can be obtained for all magnetic field values by comparing the results with those from direct numerical renormalization group and Bethe ansatz calculations.
We apply the renormalized perturbation theory (RPT) to the symmetric Anderson impurity model. Within the RPT framework exact results for physical observables such as the spin and charge susceptibility can be obtained in terms of the renormalized values $\tilde{\boldsymbolμ} = (\tildeΔ, \tilde{U})$ of the hybridization $Δ$ and Coulomb interaction $U$ of the model. The main difficulty in the RPT approach usually lies in the calculation of the renormalized values themselves. In the present work we show how this can be accomplished by deriving differential flow equations describing the evolution o…
We study the renormalized perturbation theory of the single-impurity Anderson model, particularly the high-order terms in the expansion of the self-energy in powers of the renormalized coupling $\tilde{U}$. Though the presence of counter-terms in the renormalized theory may appear to complicate the diagrammatics, we show how these can be seamlessly accommodated by carrying out the calculation order-by-order in terms of skeleton diagrams. We describe how the diagrams pertinent to the renormalized self-energy and four-vertex can be automatically generated, translated into integrals and numerical…
We extend the renormalized perturbation theory for the single impurity Anderson model to the n-channel model with a Hund's rule coupling, and show that the exact results for the spin, orbital and charge susceptibilities, as well as the leading low temperature dependence for the resistivity, are obtained by working to second order in the renormalized couplings. A universal relation is obtained between the renormalized parameters, independent of n, in the Kondo regime. An expression for the dynamic spin susceptibility is also derived by taking into account repeated quasiparticle scattering, whic…
We illustrate the renormalized perturbation expansion method by applying it to a single impurity Anderson model. Previously, we have shown that this approach gives the {\it exact} leading order results for the specific heat, spin and charge susceptibilities and leading order temperature dependence of the resistivity for this model in the Fermi-liquid regime, when carried out to second order in the renormalized interaction $\tilde U$. Here we consider the effects of higher order quasi-particle scattering and calculate the third order contributions to the $H^3$ term in the impurity magnetization…
I present briefly some facts about nonequilibrium renormalized perturbation theory, correcting recent misleading statements in [E. Muñoz, F. Zamani, L. Merker, T. A. Costi, and S. Kirchner, Journal of Physics: Conf. Series 807, 092001 (2017)], and discuss some results of this work using rSPT at equilibrium.
Using non-equilibrium renormalized perturbation theory, we calculate the conductance G as a function of temperature T and bias voltage V for an Anderson model, suitable for describing transport properties through a quantum dot. For renormalized parameters that correspond to the extreme Kondo limit, we do not find a simple scaling formula beyond a quadratic dependence in T and V. However, if valence fluctuations are allowed, we find agreement with recent experiments.
The infinite-$U$ Anderson-Holstein impurity model is studied with a focus on the interplay between the strong electron correlation and the weak electron-phonon interaction. The slave boson method has been employed in combination with the large degeneracy expansion (1/N) technique. The charge and spin susceptibilities and the phonon propagator are obtained in the approximation scheme where the saddle point configuration and the Gaussian 1/N fluctuations are taken into account. The spin susceptibility is found not to be renormalized by electron-phonon interaction, while the charge susceptibility…
We show that the low energy behaviour of quite diverse impurity systems can be described by a single renormalized Anderson model, with three parameters, an effective level $\tildeε_d$, an effective hybridization $\tilde V$, and a quasiparticle interaction $\tilde U$. The renormalized parameters are calculated as a function of the bare parameters for a number of impurity models, including those with coupling to phonons and a Falikov-Kimball interaction term. In the model with a coupling to phonons we determine where the interaction of the quasiparticles changes sign as a function of the electro…
We study the ground-state properties of an extended periodic Anderson model to understand the role of Hund's coupling between localized and itinerant electrons using the density-matrix renormalization group algorithm. By calculating the von Neumann entropies we show that two phase transitions occur and two new phases appear as the hybridization is increased in the symmetric half-filled case due to the competition between Kondo-effect and Hund's coupling. In the intermediate phase, which is bounded by two critical points, we found a dimerized ground state, while in the other spatially homogeneo…
In recent work we have shown that the Fermi liquid aspects of the strong coupling fixed point of the s-d and Anderson models can brought out more clearly by interpreting the fixed point as a renormalized Anderson model, characterized by a renormalized level $\tildeε_d$, resonance width, $\tildeΔ$, and interaction $\tilde U$, and a simple prescription for their calculation was given using the numerical renormalization group (NRG). These three parameters completely specify a renormalized perturbation theory (RPT) which leads to exact expressions for the low temperature behaviour. Using a combina…
Studies of the effects of the Hund's rule coupling J_H in multiple orbit impurities or quantum dots using different models have led to quite different predictions for the Kondo temperature T_K as a function of J_H. We show that the differences depend on whether or not the models conserve orbital angular momentum about the impurity site. Using numerical renormalization group (NRG) calculations, we deduce the renormalized parameters for the Fermi liquid regime, and show that, despite the differences between the models, the low energy fixed point in the strong correlation regime is universal with…
We study the single channel (compactified) models, the sigma-tau model and the O(3) symmetric Anderson model, which were introduced by Coleman et al., and Coleman and Schofield, as a simplified way to understand the low energy behaviour of the isotropic and anisotropic two channel Kondo systems. These models display both Fermi liquid and marginal Fermi liquid behaviour and an understanding of the nature of their low energy fixed points may give some general insights into the low energy behaviour of other strongly correlated systems. We calculate the excitation spectrum at the non-Fermi liquid …
We study non-equilibrium current fluctuations through a quantum dot, which includes a ferromagnetic Hund's rule coupling $J$, in the low-energy Fermi liquid regime using the renormalized perturbation theory. The resulting cumulant for the current distribution in the particle-hole symmetric case, shows that spin-triplet and spin-singlet pairs of quasiparticles are formed in the current due to the Hund's rule coupling and these pairs enhance the current fluctuations. In the fully screened higher-spin Kondo limit, the Fano factor takes a value $F_b = (9M+6)/ (5M+4)$ determined by the orbital dege…
The magnetic properties of the two-channel periodic Anderson model for uranium ions, comprised of a quadrupolar and a magnetic doublet are investigated through the crossover from the mixed-valent to the stable moment regime using dynamical mean field theory. In the mixed-valent regime ferromagnetism is found for low carrier concentration on a hyper-cubic lattice. The Kondo regime is governed by band magnetism with small effective moments and an ordering vector $\q$ close to the perfect nesting vector. In the stable moment regime nearest neighbour anti-ferromagnetism dominates for less than hal…
In earlier work we showed how the low energy behavior of the symmetric Anderson model in a magnetic field $H$ could be described in terms of field dependent renormalized quasiparticles. Here we extend the approach to the non-symmetric Anderson impurity model and to the infinite dimensional Hubbard model within the DMFT approach. We present NRG results for the local spectral densities and the local longitudinal and transverse dynamic spin susceptibilities for the different parameter regimes and a sequence of values of the magnetic field. We calculate the renormalized parameters for the quasipar…
The O(3) symmetric Anderson model is an example of a system which has a stable low energy marginal Fermi liquid fixed point for a certain choice of parameters. It is also exactly equivalent, in the large U limit, to a localized model which describes the spin degrees of freedom of the linear dispersion two channel Kondo model. We first use an argument based on conformal field theory to establish this precise equivalence with the two channel model. We then use the numerical renormalization group (NRG) approach to calculate both one-electron and two-electron response functions for a range of valu…
Using renormalized perturbation theory in the Coulomb repulsion, we derive an analytical expression for the leading term in the temperature dependence of the conductance through a quantum dot described by the impurity Anderson model, in terms of the renormalized parameters of the model. Taking these parameters from the literature, we compare the results with published ones calculated using the numerical renormalization group obtaining a very good agreement. The approach is superior to alternative perturbative treatments. We compare in particular to the results of a simple interpolative perturb…
We extend the renormalized quasiparticle description of the symmetric Anderson model in a magnetic field $H$, developed in earlier work, to the non-symmetric model. The renormalized parameters are deduced from the low energy NRG fixed point for arbitrary field values. We find quasiparticle resonance widths, $\tildeΔ_σ(H)$, which depend in general on the spin $σ$ 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 quasipar…
The anomalous low energy behaviour observed in metals with strong electron correlation, such as in the heavy fermion materials, is believed to arise from the scattering of the itinerant electrons with low energy spin fluctuations. In systems with magnetic impurities this scattering leads to the Kondo effect and a low energy renormalized energy scale, the Kondo temperature $T_{\rm K}$. It has been generally assumed that these low energy scales can only be accessed by a non-perturbative approach due to the strength of the local inter-electron interactions. Here we show that it is possible to cir…
Using a slave boson representation of multi-band Hubbard models, we investigate a two-band model relevant to layered perovskites in the vicinity of half-filling. Beside the strong influence of the Hund's rule coupling, we obtain that the phase diagram separates into two regions: a weak to moderate coupling region where the effective mass is weakly renormalized, and a strong coupling regime where it is strongly renormalized. The transition between these two regimes is very sharp. It takes place in a (vanishingly) small domain. A ferromagnetic instability in only found in the strongly correlated…
We apply a two-particle semi-analytic approach to a single Anderson impurity attached to two biased metallic leads. The theory is based on reduced parquet equations justified in critical regions of singularities in the Bethe-Salpeter equations. It offers a way to treat one-particle and two-particle thermodynamic and spectral quantities on the same footing. The two-particle vertices are appropriately renormalized so that spurious transitions into the magnetic state of the weak-coupling approximations are suppressed. The unphysical hysteresis loop in the current-voltage characteristics is thereb…
We analyze a microscopic origin of the Kondo effect-assisted orbital order in heavy-fermion materials. By studying the periodic two-orbital Anderson model with two local electrons, we show that frustration of Hund's rule coupling due to the Kondo effect leads to an incommensurate spiral orbital and magnetic order, which exists only inside the Kondo screened (heavy-electron) phase. This spiral state can be observed in neutron and resonant X-ray scattering measurements in ${\rm U}$- and ${\rm Pr}$-based heavy-fermion compounds, and realized in cold atomic gases, e.g. fermionic ${}^{173}{\rm Yb}$…
In this paper a recently developed projector-based renormalization method (PRM) for many-particle Hamiltonians is applied to the periodic Anderson model (PAM) with the aim to describe heavy Fermion behavior. In this method high-energetic excitation operators instead of high energetic states are eliminated. We arrive at an effective Hamiltonian for a quasi-free system which consists of two non-interacting heavy-quasiparticle bands. The resulting renormalization equations for the parameters of the Hamiltonian are valid for large as well as small degeneracy $ν_f$ of the angular momentum. An expan…
We have applied the recently developed dual fermion technique to the spectral properties of single-band Anderson impurity problem (SIAM). In our approach a series expansion is constructed in vertices of the corresponding atomic Hamiltonian problem. This expansion contains a small parameter in two limiting cases: in the weak coupling case ($U/t \to 0$), due to the smallness of the irreducible vertices, and near the atomic limit ($U/t \to \infty$), when bare propagators are small. Reasonable results are obtained also for the most interesting case of strong correlations ($U \approx t$). The atomi…
We study low-energy properties of the N-fold degenerate Anderson model. Using a scaling that takes u=(N-1) U as an independent variable in place of the Coulomb interaction U, the perturbation series in U is reorganized as an expansion in powers of 1/(N-1). We calculate the renormalized parameters, which characterize the Kondo state, to the next leading order in the 1/(N-1) expansion at half-filling. The results, especially the Wilson ratio, agree very closely with the exact numerical renormalization group results at N=4. This ensures the applicability of our approach to N > 4, and we present h…
The Mott-Hubbard metal-insulator transition is investigated in a two-band Hubbard model within dynamical mean-field theory. To this end, we use a suitable extension of Wilson's numerical renormalization group for the solution of the effective two-band single-impurity Anderson model. This method is non-perturbative and, in particular, allows to take into account the full exchange part of the Hund's rule coupling between the two orbitals. We discuss in detail the influence of the various Coulomb interactions on thermodynamic and dynamic properties, for both the impurity and the lattice model. Th…
We apply recently developed 1/(N-1) expansion to a particle-hole asymmetric SU(N) Anderson model with finite Coulomb interaction U. To leading order in 1/(N-1) it describes the Hartree-Fock random phase approximation (HF-RPA), and the higher-order corrections describe systematically the fluctuations beyond the HF-RPA. We show that the next-leading order results of the renormalized parameters for the local Fermi-liquid state agree closely with the numerical renormalization group results at N=4. It ensures the reliability of the next-leading order results for N>4, and we examine the N dependence…
Exact formulas of diagonal conductivity $σ_{xx}$ and Hall conductivity $σ_{xy}$ are derived from the Kubo formula in hybridized two-orbital systems with arbitrary band dispersions. On the basis of the theoretical framework for the Fermi liquid based on these formulas, the ground-state properties of the periodic Anderson model with electron correlation and weak impurity scattering are studied on the square lattice. It is shown that imbalance of the mass-renormalization factors in $σ_{xx}$ and $σ_{xy}$ causes remarkable increase in the valence-fluctuation regime as the f level increases while th…
We find the emergence of strong correlations and universality on the approach to the quantum critical points of a two impurity Anderson model. The two impurities are coupled by an inter-impurity exchange interaction $J$ and direct interaction $U_{12}$ and are hybridized with separate conduction channels.The low energy behavior is described in terms of renormalized parameters, which can be deduced from numerical renormalization group (NRG) calculations. We show that on the approach to the transitions to a local singlet and a local charged ordered state, the quasiparticle weight factor $z\to 0$,…
The Anderson model of a twofold spin degenerate impurity level in the limit of infinite Coulomb repulsion, $U \to \infty$, coupled to one and two degenerate conduction bands or channels, is considered in pseudo-particle representation. We extend the Conserving T-Matrix Approximation (CTMA), a general diagrammatic approximation scheme based on a fully renormalized computation of two-particle vertex functions in the spin and in the charge channel, to the calculation of thermodynamic and spectral properties. In the single-channel case, the CTMA yields in the Kondo regime a temperature independent…
We discuss a mechanism of real-space spin-triplet pairing, alternative to that due to quantum paramagnon excitations, and demonstrate its applicability to $\mathrm{UGe_2}$. Both the Hund's rule ferromagnetic exchange and inter-electronic correlations contribute to the same extent to the equal-spin pairing, particularly in the regime in which the weak-coupling solution does not provide any. The theoretical results, obtained within the orbitally-degenerate Anderson lattice model, match excellently the observed phase diagram for $\mathrm{UGe_2}$ with the coexistent ferromagnetic (FM1) and superco…
We study the competition between Kondo physics and dissipation within an Anderson model of a magnetic impurity level that hybridizes with a metallic host and is also coupled, via the impurity charge, to the displacement of a bosonic bath having a spectral density proportional to ω^s. As the impurity-bath coupling increases from zero, the effective Coulomb interaction between two electrons in the impurity level is progressively renormalized from its repulsive bare value until it eventually becomes attractive. For weak hybridization, this renormalization in turn produces a crossover from a conve…
We study the competition of Coulomb interaction and hybridization effects in the five-orbital Anderson impurity model by means of continuous time quantum Monte Carlo, exact diagonalization, and Hartree Fock calculations. The dependence of the electronic excitation spectra and thermodynamic ground state properties on hybridization strength and the form of the Coulomb interaction is systematically investigated for impurity occupation number $N \approx 6$. With increasing hybridization strength, a Kondo resonance emerges, broadens and merges with some of the upper and lower Hubbard peaks. Concomi…
A modified version of the spinless Anderson model is studied by means of the continuous-time quantum Monte Carlo method. This study is motivated by the peculiar heavy-fermion behavior observed in certain Samarium compounds, which is insensitive to magnetic field. The model involves M channels for conduction electrons, all of which interact with local f electron via the Coulomb repulsion Ufc, while only one channel has hybridization with the local state. The effective hybridization is reduced by the Anderson orthogonality effect, and a quantum critical point occurs with increasing M and/or incr…
Recently proposed local-correlation-driven pairing mechanism, describing ferromagnetic phases (FM1 and FM2) coexisting with spin-triplet superconductivity (SC) within a single orbitally degenerate Anderson lattice model, is extended to the situation with applied Zeeman field. The model provides and rationalizes in a semiquantitative manner the principal features of the phase diagram observed for $\mathrm{UGe_2}$ in the field absence [cf. Phys. Rev. B $\mathbf{97}$, 224519 (2018)]. As spin-dependent effects play a crucial role for both the ferromagnetic and SC states, the role of the Zeeman fie…
We study the three-orbital Kondo effect in quantum dot (QD) systems by applying the non-crossing approximation to the three-orbital Anderson impurity model. By investigating the tunneling conductance through a QD, we show that the competition between the Hund-coupling and the orbital level-splitting gives rise to characteristic behavior in transport properties. It is found that the Hund-coupling becomes more important in the three-orbital case than in the two-orbital case. We also show that the enhancement of Kondo temperature due to the singlet-triplet mechanism suggested for the two-orbital …
We review here some universal aspects of the physics of two-electron molecular transistors in the absence of strong spin-orbit effects. Several recent quantum dots experiments have shown that an electrostatic backgate could be used to control the energy dispersion of magnetic levels. We discuss how the generically asymmetric coupling of the metallic contacts to two different molecular orbitals can indeed lead to a gate-tunable Hund's rule in the presence of singlet and triplet states in the quantum dot. For gate voltages such that the singlet constitutes the (non-magnetic) ground state, one ge…
