Mott transition of fermionic atoms in a three-dimensional optical trap

We study theoretically the Mott metal-insulator transition for a system of fermionic atoms confined in a three-dimensional optical lattice and a harmonic trap. We describe an inhomogeneous system of several thousand sites using an adaptation of dynamical mean field theory solved efficiently with the numerical renormalization group method. Above a critical value of the on-site interaction, a Mott-insulating phase appears in the system. We investigate signatures of the Mott phase in the density profile and in time-of-flight experiments.Comment: 4 pages and 5 figure

Magnetotransport through a strongly interacting quantum dot

We study the effect of a magnetic field on the conductance through a strongly interacting quantum dot by using the finite temperature extension of Wilson's numerical renormalization group method to dynamical quantities. The quantum dot has one active level for transport and is modelled by an Anderson impurity attached to left and right electron reservoirs. Detailed predictions are made for the linear conductance and the spin-resolved conductance as a function of gate voltage, temperature and magnetic field strength. A strongly coupled quantum dot in a magnetic field acts as a spin filter which can be tuned by varying the gate voltage. The largest spin-filtering effect is found in the range of gate voltages corresponding to the mixed valence regime of the Anderson impurity model.Comment: Revised version, to appear in PRB, 4 pages, 4 figure

Transport Coefficients of the Anderson Model via the Numerical Renormalization Group

The transport coefficients of the Anderson model are calculated by extending Wilson's NRG method to finite temperature Green's functions. Accurate results for the frequency and temperature dependence of the single--particle spectral densities and transport time $\tau(\omega,T)$ are obtained and used to extract the temperature dependence of the transport coefficients in the strong correlation limit. The low temperature anomalies in the resistivity, $\rho(T)$, thermopower, $S(T)$, thermal conductivity $\kappa(T)$ and Hall coefficient, $R_{H}(T)$, are discussed. All quantities exhibit the expected Fermi liquid behaviour at low temperature with power law dependecies on $T/T_{K}$ in very good agreement with analytic results based on Fermi liquid theory. Scattering of conduction electrons in higher, $l>0$, angular momentum channels is also considered and an expression is derived for the corresponding transport time and used to discuss the influence of non--resonant scattering on the transport properties.Comment: 45 pages, RevTeX, 28 figures, available on reques

Real-Time-RG Analysis of the Dynamics of the Spin-Boson Model

Using a real-time renormalization group method we determine the complete dynamics of the spin-boson model with ohmic dissipation for coupling strengths $\alpha\lesssim 0.1-0.2$. We calculate the relaxation and dephasing time, the static susceptibility and correlation functions. Our results are consistent with quantum Monte Carlo simulations and the Shiba relation. We present for the first time reliable results for finite cutoff and finite bias in a regime where perturbation theory in $\alpha$ or in tunneling breaks down. Furthermore, an unambigious comparism to results from the Kondo model is achieved.Comment: 4 pages, 5 figures, 1 tabl

The numerical renormalization group method for quantum impurity systems

In the beginning of the 1970's, Wilson developed the concept of a fully non-perturbative renormalization group transformation. Applied to the Kondo problem, this numerical renormalization group method (NRG) gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin. The NRG has been later generalized to a variety of quantum impurity problems. The purpose of this review is to give a brief introduction to the NRG method including some guidelines of how to calculate physical quantities, and to survey the development of the NRG method and its various applications over the last 30 years. These applications include variants of the original Kondo problem such as the non-Fermi liquid behavior in the two-channel Kondo model, dissipative quantum systems such as the spin-boson model, and lattice systems in the framework of the dynamical mean field theory.Comment: 55 pages, 27 figures, submitted to Rev. Mod. Phy

Kondo proximity effect: How does a metal penetrate into a Mott insulator?

We consider a heterostructure of a metal and a paramagnetic Mott insulator using an adaptation of dynamical mean field theory to describe inhomogeneous systems. The metal can penetrate into the insulator via the Kondo effect. We investigate the scaling properties of the metal-insulator interface close to the critical point of the Mott insulator. At criticality, the quasiparticle weight decays as 1/x^2 with distance x from the metal within our mean field theory. Our numerical results (using the numerical renormalization group as an impurity solver) show that the prefactor of this power law is extremely small.Comment: 4 pages, 3 figure

Scaling and universality in the anisotropic Kondo model and the dissipative two-state system

Scaling and universality in the Ohmic two-state system is investigated by exploiting the equivalence of this model to the anisotropic Kondo model. For the Ohmic two-state system, we find universal scaling functions for the specific heat, $C_{\alpha}(T)$, static susceptibility, $\chi_{\alpha}(T)$, and spin relaxation function $S_{\alpha}(\omega)$ depending on the reduced temperature $T/\Delta_{r}$ (frequency $\omega/\Delta_{r}$), with $\Delta_{r}$ the renormalized tunneling frequency, and uniquely specified by the dissipation strength $\alpha$ ($0<\alpha<1$). The scaling functions can be used to extract $\alpha$ and $\Delta_{r}$ in experimental realizations.Comment: 5 pages (LaTeX), 4 EPS figures. Minor changes, typos corrected, journal reference adde

Anderson impurity model at finite Coulomb interaction U: generalized Non-crossing Approximation

We present an extension of the non-crossing approximation (NCA), which is widely used to calculate properties of Anderson impurity models in the limit of infinite Coulomb repulsion $U\to\infty$, to the case of finite $U$. A self-consistent conserving pseudo-particle representation is derived by symmetrizing the usual NCA diagrams with respect to empty and doubly occupied local states. This requires an infinite summation of skeleton diagrams in the generating functional thus defining the ``Symmetrized finite-U NCA'' (SUNCA). We show that within SUNCA the low energy scale $T_K$ (Kondo temperature) is correctly obtained, in contrast to other simpler approximations discussed in the literature.Comment: 7 pages, 6 figure

Renormalization Group Approach to Non-equilibrium Green Functions in Correlated Impurity Systems

We present a technique for calculating non-equilibrium Green functions for impurity systems with local interactions. We use an analogy to the calculation of response functions in the x-ray problem.The initial state and the final state problems, which correspond to the situations before and after the disturbance (an electric or magnetic field, for example) is suddenly switched on, are solved with the aid of Wilson's momentum shell renormalization group. The method is illustrated by calculating the non-equilibrium dynamics of the ohmic two-state problem.Comment: 7 pages, 2 figure

Unified description of Fermi and non-Fermi liquid behavior in a conserving slave boson approximation for strongly correlated impurity models

We show that the presence of Fermi or non-Fermi liquid behavior in the SU(N) x SU(M) Anderson impurity models may be read off the infrared threshold exponents governing the spinon and holon dynamics in a slave boson representation of these models. We construct a conserving T-matrix approximation which recovers the exact exponents with good numerical accuracy. Our approximation includes both coherent spin flip scattering and charge fluctuation processes. For the single-channel case the tendency to form bound states drastically modifies the low energy behavior. For the multi-channel case in the Kondo limit the bound state contributions are unimportant.Comment: 4 pages, Latex, 3 postscript figures included Final version with minor changes in wording, to appear in Phys.Rev.Let