### 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### Renormalisation Group Approaches to Strongly Correlated Electron-Phonon Systems

**Authors:**A.C. Hewson

**published in:**Proceedings of the Inernational 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### 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### 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