### Analysis of low energy response and possible emergent SU(4) Kondo state in a double quantum dot

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

**accepted for publication in**Physical Review B (2013)

We examine the low energy behavior of a double quantum dot in a regime where spin and pseudospin excitations are degenerate. The individual quantum dots are described by Anderson impurity models with an on-site interaction U which are capacitively coupled by an interdot interaction U12 < U. The low energy response functions are expressed in terms of renormalized parameters, which can be deduced from an analysis of the fixed point in a numerical renormalization group calculation. At the point where the spin and pseudospin degrees of freedom become degenerate, the free quasiparticle excitations have a phase shift of pi/4 and a 4-fold degeneracy. We find, however, when the quasiparticle interactions are included, that the low energy effective model has SU(4) symmetry only in the special case U12 = U unless both U and U12 are greater than D, the half-bandwidth of the conduction electron bath. We show that the gate voltage dependence of the temperature dependent differential conductance observed in recent experiments can be described by a quasiparticle density of states with temperature dependent renormalized parameters.

Available on Cond-Mat Archive### Extremely correlated Fermi liquid study of the U =infinity Anderson impurity model

**Authors:**B.S. Shastry, E. Perepelitsky and A.C. Hewson

**published in**Physical Review B**88**205108 (2013)

We apply the recently developed extremely correlated Fermi liquid (ECFL) theory to the Anderson impurity model, in the extreme correlation limit U -> infinity. We develop an expansion in a parameter lambda, related to nd, the average occupation of the localized orbital, and find analytic expressions for the Greens functions to order lambda squared. These yield the impurity spectral function and also the self-energy in terms of the two self-energies of the ECFL formalism. The imaginary parts of the latter have roughly symmetric low-energy behavior (proportional to omega squared), as predicted by Fermi liquid theory. However, the inferred impurity self-energy develops asymmetric corrections near nd --> 1, leading in turn to a strongly asymmetric impurity spectral function with a skew towards the occupied states. Within this approximation, the Friedel sum rule is satisfied but we overestimate the quasiparticle weight z relative to the known exact results, resulting in an overbroadening of the Kondo peak. Upon scaling the frequency by the quasiparticle weight z, the spectrum is found to be in reasonable agreement with numerical renormalization group results over a wide range of densities.

Available on Cond-Mat Archive

### 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.

Available on Cond-Mat Archive### Hunds 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 Hunds rule term, JH = 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 Hunds 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 Hunds 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.G.J. 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### Kondo effects in a triangular triple quantum dot: Numerical renormalization group study in the whole region of the electron filling

**Authors:**A. Oguri, S. Amaha, Y. Nishikawa, T. Numata, M. Shimamoto, A.C. Hewson and S. Tarucha

We study the low-energy properties and characteristic Kondo energy scale of a triangular triple quantum dot, connected to two non-interacting leads, in a wide parameter range of a gate voltage and distortions which lower the symmetry of an equilateral structure, using the numerical renormalization group approach. For large Coulomb interactions, the ground states with different characters can be classified according to the plateaus of $\Theta$ (e݆o)(2/), where e and o are the phase shifts for the even and odd partial waves. At these plateaus of $\Theta$, both $\Theta$ and the occupation number Ntot (e + o)(2/) take values close to integers, and thus the ground states can be characterized by these two integers. The Kondo effect with a local moment with total spin S = 1 due to a Nagaoka mechanism appears on the plateau, which can be identified by $\Theta$ %G≃%@ 2.0 and Ntot %G≃%@ 4.0. For large distortions, however, the high-spin moment disappears through a singlet-triplet transition occurring within the four-electron region. It happens at a crossover to the adjacent plateaus for $\Theta$ %G≃%@ 0.0 and $\Theta$ %G≃%@ 4.0, and the two-terminal conductance has a peak in the transient regions. For weak distortions, the SU(4) Kondo effect also takes place for Ntot %G≃%@ 3.0. It appears as a sharp conductance valley between the S = 1/2 Kondo ridges on both sides. We also find that the characteristic energy scale T %G∗%@ reflect these varieties of the Kondo effect. Particularly, T %G∗%@ is sensitive to the distribution of the charge and spin in the triangular triple dot.

Available on Cond-Mat Archive### Competition between antiferromagnetism and charge order in Hubbard-Holstein model

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

**published in:**Physical Review B**81**235113 (2010)

We study the competition between an instantaneous local Coulomb repulsion and a boson mediated retarded attraction, as described by the Hubbard-Holstein model. Restricting to the case of half-filling, the ground-state phase diagram and the transitions from antiferromagnetically ordered states to charge ordered states are analyzed. The calculations are based on the model in large dimensions, so that dynamical mean-field theory can be applied, and the associated impurity problem is solved using the numerical renormalization group method. The transition is found to occur when electron-electron coupling strength U and the induced interaction $\lambda$ due to electron-phonon coupling approximately coincide, $U\approx \lambda$. We find a continuous transition for small coupling and large $\omega_0$, and a discontinuous one for large coupling and/or small $\omega_0$. We present results for the order parameters, the static expectation values for the electrons and phonons, and the corresponding spectral functions. They illustrate the different types of behavior to be seen near the transitions. Additionally, the quasiparticle properties are calculated in the normal state, which leads to a consistent interpretation of the low-energy excitations.

Available on Cond-Mat Archive### A quantum phase transition between antiferromagnetism and charge order in a Hubbard-Holstein model

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

**published in:**Physica Status Solidi**247**638 (2010)

We explore the quantum phase transitions between two ordered states in the infinite dimensional Hubbard-Holstein model at half filling. Our study is based on the dynamical mean field theory (DMFT) combined with the numerical renormalization group (NRG), which allows us to handle both strong electron-electron and strong electron-phonon interactions. The transition line is characterized by an effective electron-electron interaction. Depending on this effective interaction and the phonon frequency $\omega$ one finds either a continuous transition or discontinuous transition. Here, the analysis focuses on the behavior of the system when the electron-electron repulsion U and the phonon-mediated attraction $\lambda$ are equal. We first discuss the adiabatic and antiadiabatic limiting cases. For finite $\omega$ we study the differences between the antiferromagnetic (AFM) and charge order, and find that when present the AFM state has a lower energy on the line.

Available on Cond-Mat Archive### A numerical renormalization group study of probability distributions of local fluctuations in the Anderson-Holstein and Hubbard-Holstein models

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

**published in:**J. Physics: Condens. Matter**22**115602 (2010)

We show that information on the probability density of local fluctuations can be obtained from a numerical renormalization group calculation of a reduced density matrix. We apply this approach to the Anderson%G–%@Holstein impurity model to calculate the ground state probability density (x) for the displacement x of the local oscillator. From this density we can deduce an effective local potential for the oscillator and compare its form with that obtained from a semiclassical approximation as a function of the coupling strength. The method is extended to the infinite dimensional Holstein%G–%@Hubbard model using dynamical mean field theory. We use this approach to compare the probability densities for the displacement of the local oscillator in the normal, antiferromagnetic and charge ordered phases.

Available on Cond-Mat Archive### Renormalized Perturbation Approach to Electron Transport through Quantum Dots

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

**to be published in:**Proceedings of the workshop on 'Physical Properties of Nanosystems', Yalta

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### Kondo effects in a triangular triple quantum dot: Numerical renormalization group study in the whole region of the electron filling

**Authors:**T. Numata, Y. Nishikawa, A. Oguri and A.C. Hewson

**published in:**Physical Review B**80**155330 (2009)

This is a study of a triangular quntum dot using the NRG. Various kinds of Kondo effects take place in this system depending on the electron filling N_{tot}, or the level position $\epsilon_d$ of the triple dot. The SU(4) Kondo behavior is seen in the half-filled case N_{tot} = 3.0 at the dip of the series conductance, and it causes a charge redistribution between the even and odd orbitals in the triangle. We show generally that the quasi-particle excitations from a local Fermi-liquid ground state acquire a channel symmetry at zero points of the two-terminal conductance, in the case the system has time-reversal and inversion symmetries. It causes the SU(4) behavior at low energies, while the orbital degeneracy in the triangle determines the high-energy behavior. At four-electron filling N_{tot} = 4.0, a local S=1 moment emerges at high temperatures due to a Nagaoka ferromagnetic mechanism. It is fully screened by the electrons from the two conducting channels via a two-stage Kondo effect, which is caused by a difference in the charge distribution in the even and odd orbitals.

Available on Cond-Mat Archive### DMFT-NRG for superconductivity in the attractive Hubbard model

**Authors:**J. Bauer, A.C. Hewson, N. Dupuis

**published in:**Physical Review B**79**214518 (2009)

This is a study of the attractive Hubbard model based on the dynamical mean field theory (DMFT) combined with the numerical renormalization group (NRG). For this study the NRG method is extended to deal with self-consistent solutions of effective impurity models with superconducting symmetry breaking. We give details of this extension and validate our calculations with DMFT results with antiferromagnetic ordering. We also present results for static and integrated quantities for different filling factors in the crossover from weak (BCS) to strong coupling (BEC) superfluidity. The main focus is the evolution of the single particle spectra throughout the whole crossover regime. We find that the sharp quasiparticle peaks at weak coupling transform continuously to an asymmetric incoherent spectrum at strong coupling. This behavior can be understood in terms of the diagonal and offdiagonal self-energies with their full frequency dependence.

Available on Cond-Mat Archive### Quasiparticle excitations and dynamic susceptibilities in the BCS-BEC crossover

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

**published in:**Euro. Phys. Lett.**85**27001 (2009)

The dynamic ground state properties in the crossover from weak (BCS) to strong coupling (BEC) superfluidity are studied. The approach is based on the attractive Hubbard model which is analyzed by the dynamical mean field theory (DMFT) combined with the numerical renormalization group (NRG). We present an extension of the NRG method for effective impurity models to selfconsistent calculations with superconducting symmetry breaking. In the one particle spectra we show quantitatively how the Bogoliubov quasiparticles at weak coupling become suppressed at intermediate coupling. We also present results for the spin and charge gap. The extension of the NRG method to selfconsistent superconducting solutions opens the possibility to study a range of other important applications.

Available on Cond-Mat Archive### Gate-voltage dependence of the Kondo effect in a traingular quantum dot

**Authors:**T. Numata, Y. Nisikawa, A. Oguri, A. C. Hewson

This ia a study the conductance through a triangular triple quantum dot, which are connected to two noninteracting leads. The calculations are performed using the numerical renormalization group (NRG). It is found that the system shows a variety of Kondo effects depending on the filling of the triangle. The SU(4) Kondo effect occurs at half-filling, and a sharp conductance dip due to a phase lapse appears in the gate-voltage dependence. Furthermore, when four electrons occupy the three sites on average, a local S=1 moment, which is caused by the Nagaoka mechanism, is induced along the triangle. The temperature dependence of the entropy and spin susceptibility of the triangle shows that this moment is screened by the conduction electrons via two separate stages at different temperatures. The two-terminal and four-terminal conductances show a clear difference at the gate voltages, where the SU(4) or the S=1 Kondo effects occurring.

Available on Cond-Mat Archive### Spectral properties of locally correlated electrons in a BCS superconductor

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

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

This is a detailed study of the spectral properties of a locally correlated site embedded in a BCS superconducting medium. The one and two-particle dynamic response functions are calculated to elucidate the spectral excitations and the nature of the ground state for different parameter regimes with and without particle-hole symmetry. The position and weight of the Andreev bound states is given for all relevant parameter regimes.

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

**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### Field dependent quasiparticles in the infinite dimensional Hubbard model

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

**to be 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.

Available on Cond-Mat Archive

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

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

**to be 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.

Available on Cond-Mat Archive

### Kondo effect in asymmetric Josephson couplings through a quantum dot

**Authors:**Yoshihide Tanaka, Akira Oguri, A. C. Hewson

**published in:**New Journal of Physics**9**115 (2007)

A study is made of how the asymmetry of the coupling of a quantum dot to two superconductors affects the singlet to doublet transition which occurs when the on-site interaction U reaches a critical value.

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

**Authors:**A.C. Hewson

**published in:**Proceedings of the International School of Physics "Enrico Fermi"**CLXI**155 (2006)

These are lectures were given at the Enrico Fermi Summer School, Varenna, 2005. They survey how the numerical renormalisation group approach has been used to look at problems which involve strong electron-phonon interactions. A number of results of calculations of this type for the Hubbard-Holstein are reviewed.

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### Singular Dynamics of Underscreened Magnetic Impurity Models

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

**published in:**Phys. Rev. B**72**045117 (2005)

We use the NRG to calculate the spectral functions for the Kondo model with spin S=1/2,1,3/2 coupled both ferromagnetically or antiferromagnetically to spins in a single conduction channel. Singular behaviour is found in all cases excepts that case of S=1/2 with antiferromagnetic coupling. The nature of the low energy NRG fixed point was analysed and shown to correspond to singular Fermi liquid, rather than non-Fermi liquid, behaviour.

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### Quantum phase transition in a minimal model for the Kondo effect in a Josephson junction

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

**published in:**Journal of the Physical Society of Japan**73**2494 (2004)

We show that the model for a quantum dot connected to two superconductors, simplifies when the superconducting gap for one of the superconductors is very large, such that it corresponds to a model connected to a single superconductor plus an additional boundary condition. The numerical renormalisation group (NRG) is used to study the Josephson current through the dot in this limit, and the singlet to doublet transition, which occurs when the interaction on the dot U reaches a critical value.

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### Dynamic response functions for the the Holstein-Hubbard model

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

**published in:**Phys. Rev. B**70**155103 (2004)

Using a combination of dynamical mean field theory (DMFT) and numerical renormalisation group (NRG) calculations, the single electron and two electron response functions were calculated in the physically different parameter regimes of the Holstein-Hubbard model at half-filling. The degree of softening of the phonon modes was in the various regimes investigated by calculating the spectral densities of the local phonon Green's functions.

Available on Cond-Mat Archive### Phase diagram and dynamic response functions of the Holstein-Hubbard model

**Authors:**W. Koller, D. Meyer, A. C. Hewson, Y. Ono

**published in:**Physica B**359-361**795 (2005)

A summary of the calculations to determine the paramagnetic metal-to-insulator transitions in the Holstein-Hubbard model, and results for the dynamic correlation functions in the different parameter regimes.

Available on Cond-Mat Archive### First- and second-order phase transitions in the Holstein-Hubbard model

**Authors:**W. Koller, D. Meyer, Y. Ono and A.C. Hewson

**published in:**Europhys. Lett.**66**559 (2004)

We show that there are two types of paramagnetic metal-to-insulator transitions in the Holstein-Hubbard model as a function of the on-site interaction U and the electron-phonon coupling g. A complete phase diagram of these transitions is presented, based on different methods of calculation, which are in good agreement.

Available on Cond-Mat Archive### Gap formation in the Holstein Model

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

**published in:**Acta Physica Polonica B**34**769 (2003)

We show how nature of the gap which opens up at the metal-to insulator transition in the half-filled Holstein model varies as a function of the frequency of the local oscillator.

### Gap formation and Soft Phonon Mode in the Holstein Model

**Authors:**D. Meyer, A.C. Hewson and R. Bulla

**published in:**Phys. Rev. Lett.**89**196401 (2002)

A study of the Holstein model using the NRG at half-filling where we show that bipolaron formation at strong coupling leads to a gap induced at the Fermi level and a metal to insulator transition.

Available on Cond-Mat Archive### Numerical renormalization group study of the Anderson-Holstein impurity model

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

**published in:**J. Phys.:Cond. Matter**14**427 (2002)

The interplay of the two types of local interaction in the Anderson-Holstein model, the on-site electron-electron repulsion and the local coupling to a phonon mode, are investigated using the NRG.

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.-
### Critical behaviour near the metal-insulator transition of a doped Mott insulator

**Authors:**Y. Ono, R. Bulla, A.C. Hewson and M.Potthoff

**published in:**European Physics Journal B**19**375 (2001)

The linearized dynamical mean field theory for the single band Hubbard model is extended to small hole and electron doping.

PostScript Version. ### 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.### Phase Diagram of the Mott Transition in a two-band Hubbard Model in Infinite Dimensions

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

**published in:**European Physics Journal B**19**375 (2001)

Analytic expressions are derived to determine the metal-insulator phase diagram for a two-band Hubbard model (d-p model) using linearized dynamical mean field theory. Checks on the results using the exact diagonalization method for solving the dynamical mean field theory suggest that the linearized form is a very good approximation with errors of less than 5%.

PostScript Version.### The effects of band dispersion and interactions on the excitation gaps in the periodic Anderson model in infinite dimensions

**Authors:**Y. Shimizu, O. Sakai and A.C. Hewson

**to be published in:**Journal of the Japanese Physical Society**69**1777 (2000)

The inter-play of f-electron dispersion and the inter-f electron interactions are investigated for the periodic Anderson model, based on dynamic mean field theory and numerical renormalization group calculations.

### 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.

### Specific Heat and Magnetization of the Impurity Anderson Model with non-Kramers Doublet Lowest State subject to a Tetragonal Crystalline Electric Field

**Authors:**Y. Shimizu, A.C. Hewson and O. Sakai

**published in:**Journal of the Japanese Physical Society**68**2994 (1999)

The specific heat and magnetization of a generalized Anderson model, which describes an f^2 configuration split by a crystalline electric field such that a non-Kramers doublet lies lowest, are calculated using the numerical renormalization group method. The model displays Fermi-liquid and also non-Fermi-liquid behaviour (corresponding to that of a two channel Kondo model), depending on the strength of the hybridization.

>### Metal-Insulator transition in the Hubbard model

**Authors:**R. Bulla, Th. Pruschke and A.C. Hewson

**published in:**Physica B**259-261**721 (1999)

This paper is a report of numerical renormalization group calculations for the infinite dimensional half-filled Hubbard model at zero temperature, using dynamic mean field theory (DMFT).

### Spectral Densities for the O(3) Anderson Model

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

**published in:**Physica B**259-261**362 (1999)

Preliminary results of numerical renormalization group calculations for the T=0 spectral densities of the response functions of the the O(3) Anderson model are reported.

### Numerical renormalization group calculations for the self-energy of the impurity Anderson model

**Authors:**R. Bulla (1), A.C. Hewson (2) and Th. Pruschke (3), ((1) Imperial College, London, (2) MPIPKS Dresden, (3) Universität Regensburg)

**published in:**J. Phys.: Condens. Matter**10**, 8365-8380 (1998)

We present a new method for calculating directly the one-particle self-energy of an impurity Anderson model with Wilson's numerical renormalization group method by writing this quantity as the ratio of two correlation functions. This way of calculating the self-energy turns out to be considerably more reliable and accurate than that via the impurity Green's function alone. We give results for the self-energy for the case of a constant coupling between the impurity and the conduction electron band, and the effective energy dependent coupling arising in the dynamical mean-field theory of the Hubbard model. The implications of the problem of the meta-insulator transition in the Hubbard model are also discussed.

PostScript Version### Anderson impurity in pseudo-gap Fermi systems

**Authors:**R. Bulla (1), Th. Pruschke (2), A. C. Hewson (1) ((1) Imperial College, London, (2) Universität Regenburg)

**published in:**J. Phys.: Condens. Matter**9**, 10463 (1997)

We use the numerical renormalization group method to study an Anderson impurity in a conduction band with the density of states varying as rho(omega) \propto |omega|^r with r>0. We find two different fixed points: a local-moment fixed point with the impurity effectively decoupled from the band and a strong-coupling fixed point with a partially screened impurity spin. The specific heat and the spin-susceptibility show powerlaw behaviour with different exponents in strong-coupling and local-moment regime. We also calculate the impurity spectral function which diverges (vanishes) with |omega|^{-r} (|\omega|^r) in the strong-coupling (local moment) regime.

### Exact equivalence of linear dispersion two channel Kondo model and the $\sigma$-$\tau$ model

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

**published in**Solid State Comm.**112**105 (1999)

We show that a Majorana fermion description of the two channel Kondo model can emerge quite naturally as a representation of the algebra associated with the spin currents in the two channels. Using this representation we derive an exact equivalent Hamiltonian for the two channel model expressed entirely in terms of Majorana fermions. The part of the Hamiltonian that is coupled to the impurity spin corresponds to the vector part of the $\sigma$-$\tau$ model (compactified two channel model). Consequently all the thermodynamic properties associated with the impurity spin can be calculated from the $\sigma$-$\tau$ model alone. The equivalent model can be used to confirm the interpretation of the many-body excitation spectrum of the low energy fixed point of the two-channel model as due to free Majorana fermions with appropriate boundary conditions.

PostScript Version### 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.

### Numerical Renormalization Group Study of the O(3)-symmetric Anderson Model

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

**published in**: Z. Phys.B**104**, 333 (1997)

We use the numerical renormalization group method to study the O(3)-symmetric version of the impurity Anderson model of Coleman and Schofield. This model is of general interest because it displays both Fermi liquid and non-Fermi liquid behaviour, and in the large $U$ limit can be related to the compactified two channel Kondo model of Coleman, Ioffe and Tsvelik. We calculate the thermodynamics for a parameter range which covers the full range of behaviour of the model. We find a non-Fermi liquid fixed point in the isotropic case which is unstable with respect to channel anisotropy.

### Numerical Renormalization Group Study of the 'Compactified' Anderson Model

**Authors:**R. Bulla, A. C. Hewson (Imperial College, London, U.K.)**published in:**Physica B**230-232**, 627 (1997)

We use the numerical renormalization group method to study the `compactified' version of the impurity Anderson model of Coleman and Schofield. This model is of general interest because it displays both Fermi liquid and non-Fermi liquid behaviour, and in the large $U$ limit can be related to the compactified two channel Kondo model of Coleman, Ioffe and Tsvelik. We calculate the thermodynamics for a parameter range which covers the full range of behaviour of the model. We find a non-Fermi liqud fixed point in the isotropic case which is unstable with respect to channel anisotropy.

### 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.