### Renormalized perturbation theory and scaling for an impurity Anderson model

**Authors:**K.Edwards, A.C. Hewson and V. Pandis

**published in**Physical Review B**87**165128 (2013)

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.

arXiv:1303.6865 Available on Cond-Mat Archive### Hund's rule coupling in models of magnetic impurities and quantum dots

**Authors:**Y. Nishikawa and A.C. Hewson

**published in**Physical Review B**86**245131 (2012)

Different models have led to quite different predictions for the Kondo temperature TK as a function of JH. We show that the differences depend on whether or not the models conserve orbital angular momentum about the impurity site. Using numerical renormalization-group 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 a single energy scale TK and just two renormalized interaction parameters, a renormalized single orbital term, ˜U = 4TK, and a renormalized Hund’s rule term, J˜H = 8TK/3.

arXiv:1211.0363 Available on Cond-Mat Archive### Phase diagram and critical points of a double quantum dot

**Authors:**Y. Nishikawa, D.J.G. Crow and A.C. Hewson

**published in**Physical Review B**86**125134 (2012)

We apply a combination of numerical renormalization group (NRG) and renormalized perturbation theory (RPT) to a model of two quantum dots (impurities) described by two Anderson impurity models hybridized to their respective baths. The dots are coupled via a direct Coulomb interaction $U_{12}$ and a spin exchange interaction $J$. The model has two types of quantum critical points, one at $J=J_c$ to a local singlet state and one at $U_{12}=U_{12}^c$ to a locally charge ordered state. The renormalized parameters which determine the low energy behavior are calculated from the NRG. The results confirm the values predicted from the RPT on the approach to the critical points, which can be expressed in terms of a single energy scale $T^*$ in all cases. This includes cases without particle-hole symmetry, and cases with asymmetry between the dots, where there is also a transition at $J=J_c$. The results give a comprehensive quantitative picture of the behavior of the model in the low energy Fermi liquid regimes, and some of the conclusions regarding the emergence of a single energy scale may apply to a more general class of quantum critical points, such as those observed in some heavy fermion systems.

Available on Cond-Mat Archive### Full counting statistics for orbital-degenerate impurity Anderson model with Hund's rule exchange coupling

**Authors:**Rui Sakano, Yunori Nishikawa, Akira Oguri, Alex C. Hewson, and Seigo Tarucha

**published in:**Physical Review Letters**108**266401 (2012)

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 Kondo-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 Fb = (9M + 6)/(5M + 4) determined by the orbital degeneracy M. We also investigate the crossover between the small and large J limits in the two-orbital case M = 2, using the numerical renormalization group approach.

Available on Cond-Mat Archive### A new renormalization group approach for systems with strong electron correlation

**Authors:**K. Edwards and A.C. Hewson

**published in:**J. Physics: Condens. Matter**23**045601 (2011)

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 TK. 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 circumvent this difficulty by first suppressing the spin fluctuations with a large magnetic field. As a first step field-dependent renormalized parameters are calculated using standard perturbation theory. A renormalized perturbation theory is then used to calculate the renormalized parameters for a reduced magnetic field strength. The process can be repeated and the flow of the renormalized parameters continued to zero magnetic field. We illustrate the viability of this approach for the single impurity Anderson model. The results for the renormalized parameters, which flow as a function of magnetic field, can be checked with those from numerical renormalization group and Bethe ansatz calculations.

Available on Cond-Mat Archive### Renormalized parameters and perturbation theory for the n-channel Anderson model with Hund's rule coupling: asymmetric case

**Authors:**Y. Nishikawa, D.J.G. Crow and A.C. Hewson

**published in:**Physical Review B**82**245109 (2010)

We explore the predictions of the renormalized perturbation theory for the 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 local occupation of the impurity site nd. From the exact relations in terms of the renormalized parameters, we calculate the orbital, spin 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. Some unexpected features of the results are that a strong on-site interaction gives significant renormalization and suppression charge susceptibility in the intermediate valence regimes, and the peaks in the spin susceptibility away from the particle-hole symmetric case do not occur at integer values nd=1,3

Available on Cond-Mat Archive### Renormalized parameters and perturbation theory for the n-channel Anderson model with Hund's rule coupling: symmetric case

**Authors:**Y. Nishikawa, D.J.G. Crow and A.C. Hewson

**published in:**Physical Review B**82**115123 (2010)

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, which is asymptotically exact in the low-frequency regime and satisfies the Korringa-Shiba relation. The renormalized parameters, including the renormalized Hund’s rule coupling, are deduced from numerical renormalization-group calculations for the model for the case n=2. The results confirm explicitly the universal relations between the parameters in the Kondo regime. Using these results, we evaluate the spin, orbital, and charge susceptibilities, temperature dependence of the low-temperature resistivity, and dynamic spin susceptibility for the particle-hole symmetric regime of the n =2 model.

Available on Cond-Mat Archive### Renormalized quasiparticles in antiferromagnetic states of the Hubbard model

**Authors:**A.C. Hewson, A. Oguri and J. Bauer

**published in:**Proceedings of the workshop on 'Physical Properties of Nanosystems', Yalta (Ed. J. Bonca and S. Kruchinin)

We review the basic ideas of a renormalized perturbation theory which works directly in terms of fully dressed quasiparticles, and its application to the calculation of the current through a quantum dot both in equilibrium and non-equilibrium steady state conditions. The method is illustrated for the impurity Anderson model. We show how the relevant renormalized parameters can be deduced from a numerical renormalization group calculation, and also how they can be generalized to include an arbitrary magnetic field. In applying the method to electron transmission through quantum dots, we show how the zero field conductance can be expressed in terms of the renormalized parameters, and how asymptotically exact results at low bias voltages can be derived from the expansion to second order. The potential for the further application of this approach to this class of problems is assessed.

Pdf Version### Field dependent quasiparticles in the infinite dimensional Hubbard model

**Authors:**J. Bauer and A.C. Hewson

**published in:**Phys. Rev. B**76**035118 (2007)

The description of the low energy excitations of a strongly correlated system in a magnetic field in terms of field-dependent quasiparticles is extended to the Hubbard model. The calculations are carried out using dynamical mean field theory, together with the NRG to solve the effective impurity problem. The calculations of the local dynamic spin susceptibilities calculated both directly from the NRG and via the renormalised perturbation theory are found to be in good agreement.

PDF version available

### Field dependent quasiparticles in a strongly correlated local system II

**Authors:**J. Bauer and A.C. Hewson

**published in:**Phys. Rev. B**76**035119 (2007)

The earlier calculations for quasiparticles in the Anderson model in the presence of a mangetic field are generalised to the case without particle-hole symmetry. The longitudinal and transverse dynamic spin susceptibilities are deduced from the renormalised perturbation theory and shown to be in good agreement with those calculated directly from the NRG.

PDF version available

### Spin and Charge Dynamics in a Renormalised Perturbation Theory

**Authors:**A.C. Hewson

**published in:**J. Phys.: Condens. Matter**18**1815 (2006)

We show that, by taking account of the repeated quasiparticle scattering diagrams in a renormalised perturbation theory, we can get a remarkably accurate description of the low energy spin and charge dynamical susceptibilities in all parameter regimes in the presence of a magnetic field. The renormalised parameters are deduced from the low energy NRG fixed point for the particle-hole symmetric Anderson model.

Available on Cond-Mat Archive### Magnetic Field Effects of Quasiparticles in Strongly Correlated Local System

**Authors:**A.C. Hewson, J. Bauer and W. Koller

**published in:**Phys. Rev. B**73**045117 (2006)

We show how the low energy excitations for an impurity Anderson modle in a magnetic field can be described in terms of quasiparticles with field-dependent parameters, and how to deduce these parameters from the NRG fixed point for the particle-hole symmetric Anderson model. Using these parameters in a renormalised perturbation theory we show that many response functions change sign as a function of magnetic field in the Kondo regime.

Available on Cond-Mat Archive### Polaronic Quasiparticles in a Strongly Correlated Electron Band

**Authors:**W. Koller, A.C. Hewson, and D.M. Edwards

**published in:**Phys. Rev. Lett.**95**256401 (2005)

We calculate the spectral density for the Hubbard-Holstein model in the regime away from half-filling with a strong local interaction U for increasing electron-phonon coupling strength g. We show that as g increases a narrow polaronic band develops at the Fermi level. The dispersion in this band has a kink which correlates with the softening phonon mode.

Available on Cond-Mat Archive### Non-equilibrium Differential Conductance through a Quantum Dot in a Magnetic Field

**Authors:**A.C. Hewson, J. Bauer and A. Oguri

**published in:**J. Phys.: Condens. Matter**17**5413 (2005)

We show how the leading non-linear correction to the differential conductance through a quantum dot in a magnetic field can be calculated exactly in the Kondo regime using renormalised perturbtion theory. We deduce the critical value of the field for a two peak structure to be seen in the differential conductivity as a function of bias voltage.

Available on Cond-Mat Archive### Determination of the phase shifts for interacting electrons connected to reservoirs

**Authors:**A. Oguri, Y. Nisikawa and A. C. Hewson

**published in:**Journal of the Physical Society of Japan**74**2554 (2005)

We show how one can deduce the phase shifts, and hence the T=0 conductance, for a general model from an analysis of the NRG fixed point. The method is applied to a dot corresponding to a three site Hubbard chain coupled to two non-interacting leads.

Available on Cond-Mat Archive### NRG approach to transport through a finite Hubbard chain connected to resevoirs

**Authors:**A. Oguri and A.C. Hewson

**published in:**Journal of the Physical Society of Japan**74**988 (2005)

We use the NRG to study the low energy properties of a finite Hubbard chain connected to two non-interacting reservoirs. We show how the conductance can be deduced from the approach of the NRG energy levels to the fixed point.

Available on Cond-Mat Archive### The strong coupling point revisited

**Authors:**A.C. Hewson

**published in:**Journal of the Physical Society of Japan**74**8 (2005)

We show how the low energy fixed point of the Anderson model can be analysed in terms of a renormalised version of the same model, and that these parameters can be used in a renormalised perturbation expansion, to second order in the renormalised interaction, to give the exact low temperature results in all parameter regimes.

Available on Cond-Mat Archive### Renormalized parameters for impurity models

**Authors:**A.C. Hewson, A. Oguri and D. Meyer

**published in:**The European Physical Journal B**40**177 (2004)

We show how renormalised parameters that describe the low energy quasiparticles and their interactions in a number of impurity models can be deduced from an analysis of the low energy NRG fixed point.

Available on Cond-Mat Archive### Renormalization Group Approaches to Strongly Correlated Electron Systems

**Authors:**A.C. Hewson, S.C. Bradley, R. Bulla and Y. Ono

**to be published in:**Int. Journal of Modern Physics B**15**(2001)

This is a review of applications of the numerical renormalization group technique to the dynamics of impurity models, and also, via dynamical mean field theory, to lattice models. Renormalized perturbation theory is reviewed and there is a discussion of the extent to which the parameters of the standard models should be considered as quantities which have already been renormalized.

PostScript Version.### Spectral Densities of Response Functions for the O(3) Symmetric Anderson and Two Channel Kondo model

**Authors:**S.C. Bradley, A.C. Hewson, R. Bulla and G-M Zhang

**published in:**The European Journal of Physics B**11**535 (1999)

This paper gives a full account of numerical renormalization group calculations for the T=0 dynamic response functions for the O(3) Anderson model, as well as some analytic results based on a modified renormalized perturbation theory. The equivalence of the model to that for the spin degrees of freedom for the two channel Kondo model (TCKM), in the large U limit, is used to deduce the dynamic spin susceptibility for the TCKM.

### Low energy fixed points of the sigma-tau and the O(3) symmetric Anderson models

**Authors:**R. Bulla, A. C. Hewson, G.-M. Zhang (Imperial College, London, U.K.)

**published in:**Phys. Rev. B**56**(1997) 11721

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 fixed point of the sigma-tau model using conformal field theory, and show that the results are in agreement with those obtained in recent numerical renormalization group (NRG) calculations. For the O(3) Anderson model we find further logarithmic corrections in the weak coupling perturbation expansion to those obtained in earlier calculations, such that the renormalized interaction term now becomes marginally stable rather than marginally unstable. We derive a Ward identity and a renormalized form of the perturbation theory that encompasses both the weak and strong coupling regimes and show that the chi/gamma ratio is 8/3 (chi is the total susceptibility, spin plus isospin), independent of the interaction U and in agreement with the NRG calculations.

### Renormalization group and Fermi liquid theory

**Author:**A. C. Hewson (Imperial College, London, U.K.)**published in:**Advances in Physics**43**, 543-675 (1994)

We give a Hamiltonian based interpretation of microscopic Fermi liquid theory within a renormalization group framework. The Fermi liquid fixed point Hamiltonian with its leading order corrections is identified and we show that the mean field calculations for this model correspond to the Landau phenomenological approach. This is illustrated first of all for the Kondo and Anderson models of magnetic impurities which display Fermi liquid behaviour at low temperatures. We then show how these results can be deduced by a reorganization of perturbation theory, in close parallel to that for the renormalized $\phi^4$ field theory. The Fermi liquid results follow from the two lowest order diagrams of the renormalized perturbation expansion. The calculations for the impurity models are simpler than for the general case because the self-energy depends on frequency only. We show, however, that a similar renormalized expansion can be derived also for the case of a translationally invariant system. The parameters specifying the Fermi liquid fixed point Hamiltonian are related to the renormalized vertices appearing in the perturbation theory. The collective zero sound modes appear in the quasiparticle-quasihole ladder sum of the renormalized perturbation expansion. The renormalized perturbation expansion can in principle be used beyond the Fermi liquid regime to higher temperatures. This approach should be particularly useful for heavy fermions and other strongly correlated electron systems, where the renormalization of the single particle excitations are particularly large.

Postscript Version

We briefly look at the breakdown of Fermi liquid theory from a renormalized perturbation theory point of view. We show how a modified version of the approach can be used in some situations, such as the spinless Luttinger model, where Fermi liquid theory is not applicable. Other examples of systems where Fermi liquid theory breaks down are also briefly discussed.

Convergence of Energy Scales on the Approach to a Local Quantum Critical Point

**Authors: **
Y. Nishikawa, D.J.G. Crow and A.C. Hewson

** published in: ** Physical Review Letters **108 ** 056402 (2012)

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 interimpurity exchange interaction J and direct interaction U12 and are hybridized with separate conduction channels. The low energy behavior is described in terms of renormalized parameters. We show that on the approach to the transitions to a local singlet and a local charged ordered state, the quasiparticle weight factor z→0, and the renormalized parameters can be expressed in terms of a single energy scale T*. The values of the renormalized interaction parameters in terms of T* can be predicted from the condition of continuity of the spin and charge susceptibilities, and correspond to strong correlation. These predictions are confirmed by the numerical renormalization group calculations, including the case when the on site interaction U=0.Available on Cond-Mat Archive

**Authors: **
J. Bauer and A.C. Hewson

**published in: ** Euro. Phys. J. B ** 57 ** 235 (2007)

Using a combination of dynamical mean field theory and NRG broken symmetry states, corresponding to antiferromagnetic long range order, are calculated for the Hubbard model. We show that the low energy spectral densities for these spontaneously ordered antiferromagnetic states can be described in terms of renormalised quasiparticles. The parameters for these quasiparticles can be calculated from directly from the self-energy or from the low energy fixed point of the NRG. The results of the two different types of calculation were found to be in good agreement.Available on Cond-Mat Archive

Renormalized perturbation calculations for the single impurity Anderson model

**Author:**
A.C. Hewson

** published in: **cond-mat/0106600
**15** (2001)

In this paper third order renormalized perturbation theory calculations are described for an Anderson impurity model in a magnetic field. In particular the coefficient if the third order term in the magnetization is calculated and compared with the exact Bethe ansatz result in the weak and strong coupling regimes. The result is asymptotically exact at weak coupling and very close to the exact result in the strong coupling or Kondo regime.PostScript Version.