### 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–Holstein impurity model to calculate the ground state probability density ρ(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–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### DMFT-NRG for superconductivity in the attractive Hubbard model

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

**published in**Physical Review**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### 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

**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.

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### 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.

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### 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**(2007)

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

Available on Cond-Mat Archive### 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### 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### 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.

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