Kondo effect in a magnetic field and the magnetoresistivity of Kondo alloys

The effect of a magnetic field on the spectral density of a $\rm{S=1/2}$ Kondo impurity is investigated at zero and finite temperatures by using Wilson's numerical renormalization group method. A splitting of the total spectral density is found for fields larger than a critical value $H_{c}(T=0)\approx 0.5 T_{K}$, where $T_{K}$ is the Kondo scale. The splitting correlates with a peak in the magnetoresistivity of dilute magnetic alloys which we calculate and compare with the experiments on $\rm{Ce_{x}La_{1-x}Al_{2}}, x=0.0063$. The linear magnetoconductance of quantum dots exhibiting the Kondo effect is also calculated.Comment: 4 pages, 4 eps figure

Spectral properties of a two-orbital Anderson impurity model across a non-Fermi liquid fixed point

We study by NRG the spectral properties of a two-orbital Anderson impurity model in the presence of an exchange splitting which follows either regular or inverted Hund's rules. The phase diagram contains a non-Fermi liquid fixed point separating a screened phase, where conventional Kondo effect occurs, from an unscreened one, where the exchange-splitting takes care of quenching the impurity degrees of freedom. On the Kondo screened side close to this fixed point the impurity density of states shows a narrow Kondo-peak on top of a broader resonance. This narrow peak transforms in the unscreened phase into a narrow pseudo-gap inside the broad resonance. Right at the fixed point only the latter survives. The fixed point is therefore identified by a jump of the density of states at the chemical potential. We also show that particle-hole perturbations which simply shift the orbital energies do not wash out the fixed point, unlike those perturbations which hybridize the two orbitals. Consequently the density-of-state jump at the chemical potential remains finite even away from particle-hole symmetry, and the pseudo-gap stays pinned at the chemical potential, although it is partially filled in. We also discuss the relevance of these results for lattice models which map onto this Anderson impurity model in the limit of large lattice-coordination. Upon approaching the Mott metal-insulator transition, these lattice models necessarily enter a region with a local criticality which reflects the impurity non-Fermi liquid fixed point. However, unlike the impurity, the lattice can get rid of the single-impurity fixed-point instability by spontaneously developing bulk-coherent symmetry-broken phases, which we identify for different lattice models.Comment: 43 pages, 11 figures. Minor corrections in the Appendi

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

Numerical renormalization group calculation of impurity internal energy and specific heat of quantum impurity models

We introduce a method to obtain the specific heat of quantum impurity models via a direct calculation of the impurity internal energy requiring only the evaluation of local quantities within a single numerical renormalization group (NRG) calculation for the total system. For the Anderson impurity model, we show that the impurity internal energy can be expressed as a sum of purely local static correlation functions and a term that involves also the impurity Green function. The temperature dependence of the latter can be neglected in many cases, thereby allowing the impurity specific heat, $C_{\rm imp}$, to be calculated accurately from local static correlation functions; specifically via $C_{\rm imp}=\frac{\partial E_{\rm ionic}}{\partial T} + 1/2\frac{\partial E_{\rm hyb}}{\partial T}$, where $E_{\rm ionic}$ and $E_{\rm hyb}$ are the energies of the (embedded) impurity and the hybridization energy, respectively. The term involving the Green function can also be evaluated in cases where its temperature dependence is non-negligible, adding an extra term to $C_{\rm imp}$. For the non-degenerate Anderson impurity model, we show by comparison with exact Bethe ansatz calculations that the results recover accurately both the Kondo induced peak in the specific heat at low temperatures as well as the high temperature peak due to the resonant level. The approach applies to multiorbital and multichannel Anderson impurity models with arbitrary local Coulomb interactions. An application to the Ohmic two state system and the anisotropic Kondo model is also given, with comparisons to Bethe ansatz calculations. The new approach could also be of interest within other impurity solvers, e.g., within quantum Monte Carlo techniques.Comment: 16 pages, 15 figures, published versio

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

Evaluating the expression of urokinase and tissue leukocyte being in benign and malignant breast disease

Introduction: Our objectives is to show that the expression of uPA leukocyte could be considered, in the future, as a marker of the expression of uPA in the malignant tissue and therefore a potential indicator of prognosis. Methods: We examined the expression of uPa in leukocytes and tissues of three groups of women: with breast cancer; with benign breast lesion and healthy women (control group). We used RT Real Time PCR assay. The expression of urokinase is significantly higher in malignant breast lumps compared to benign lesions. However, in women with carcinoma of the breast, malignant tissue expresses higher amounts of uPA than the healthy counterpart. There are no statistically significant differences in the expression of uPA, between tissues taken from women with benign lesions. The lymphocytes taken from healthy volunteers show a level of expression of uPA significantly lower than the other tested samples Lymphocytes extracted from cancer patients express higher amounts of uPA compared to lymphocytes belonging to women with benign breast lesions. The expression of uPA was compared with the clinical and biological parameters commonly used in clinical practice for the definition of the prognosis. The only exception found, concerns those tumors characterized by the simultaneous negativity for estrogen receptors, progesterone and HER2 (state of triple negative), in which the expression of uPA is very high. Results and conclusions: Our data show that uPA expressed by leukocytes of each individual patient is the mirror image of the one expressed by malignant nodular uPA.Introduction: Our objectives is to show that the expression of uPA leukocyte could be considered, in the future, as a marker of the expression of uPA in the malignant tissue and therefore a potential indicator of prognosis. Methods: We examined the expression of uPa in leukocytes and tissues of three groups of women: with breast cancer; with benign breast lesion and healthy women (control group). We used RT Real Time PCR assay. The expression of urokinase is significantly higher in malignant breast lumps compared to benign lesions. However, in women with carcinoma of the breast, malignant tissue expresses higher amounts of uPA than the healthy counterpart. There are no statistically significant differences in the expression of uPA, between tissues taken from women with benign lesions. The lymphocytes taken from healthy volunteers show a level of expression of uPA significantly lower than the other tested samples Lymphocytes extracted from cancer patients express higher amounts of uPA compared to lymphocytes belonging to women with benign breast lesions. The expression of uPA was compared with the clinical and biological parameters commonly used in clinical practice for the definition of the prognosis. The only exception found, concerns those tumors characterized by the simultaneous negativity for estrogen receptors, progesterone and HER2 (state of triple negative), in which the expression of uPA is very high. Results and conclusions: Our data show that uPA expressed by leukocytes of each individual patient is the mirror image of the one expressed by malignant nodular uPA

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

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

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