Many-body approach to spin-dependent transport in quantum dot systems

By means of a diagram technique for Hubbard operators, we show the existence of a spin-dependent renormalization of the localized levels in an interacting region, e.g., quantum dot, modeled by the Anderson Hamiltonian with two conduction bands. It is shown that the renormalization of the levels with a given spin direction is due to kinematic interactions with the conduction subbands of the opposite spin. The consequence of this dressing of the localized levels is a drastically decreased tunneling current for ferromagnetically ordered leads compared to that of paramagnetically ordered leads. Furthermore, the studied system shows a spin-dependent resonant tunneling behavior for ferromagnetically ordered leads.     

非对称Anderson模型的重整微扰展开

利用Yamada微扰论结合重整微扰方法来计算非对称Anderson模型,得到了局域电子占据数、重整化因子、重整化的局域能级以及重整化参数关于裸参数的展开式.计算了局域电子态密度和低温杂质电导,还计算了磁场对它们的影响,这些结果适用于从弱耦合到强耦合的整个耦合强度区域.由于在哈密顿量中已经将局域能级进行了初步重整,采用的重整微扰方法比Hewson的重整微扰方法更适合于研究非对称Anderson模型. 关键词： 非对称Anderson模型 重整化 磁场     

Generalized numerical renormalization group for dynamical quantities

In this paper we introduce a new approach for calculating dynamical properties within the numerical renormalization group. It is demonstrated that the method previously used fails for the Anderson impurity in a magnetic field due to the absence of energy scale separation. The problem is solved by evaluating the Green function with respect to the reduced density matrix of the full system, leading to accurate spectra in agreement with the static magnetization. The new procedure provides a unifying framework for calculating dynamics at any temperature and represents the correct extension of Wilson's original thermodynamic calculation.     

Isomorphism and the β-function of the non-linear σ model in symmetric spaces

The renormalization group β-function of the non-linear σ model in symmetric spaces is discussed via the isomorphic relation and the reciprocal relation about a parameter α. The four-loop term is investigated and the symmetric properties of the β-function are studied. The four-loop term in the β-function is shown to be vanishing for the orthogonal Anderson localization problem.     

Kondo resonance for orbitally degenerate systems

Formation of the Kondo state in the general two-band Anderson model has been investigated within the numerical renormalization group calculations. The Abrikosov-Suhl resonance is essentially asymmetric for the model with one electron per impurity (quarter filling case) in contrast with the one-band case. An external magnetic (pseudomagnetic) field breaking spin (orbital) degeneracy leads to asymmetric splitting and essential broadening of the many-body resonance. Unlike the standard Anderson model, the "spin-up" Kondo peak is pinned against the Fermi level, but not suppressed by the magnetic field.     

Mott-Hubbard transition and Anderson localization: A generalized dynamical mean-field theory approach

The DOS, the dynamic (optical) conductivity, and the phase diagram of a strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are taken into account by the DMFT, and disorder is taken into account via an appropriate generalization of the self-consistent theory of localization. The DMFT effective single-impurity problem is solved by a numerical renormalization group (NRG); we consider the three-dimensional system with a semielliptic DOS. The correlated metal, Mott insulator, and correlated Anderson insulator phases are identified via the evolution of the DOS and dynamic conductivity, demonstrating both the Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of the complete zero-temperature phase diagram of the Anderson-Hubbard model. Rather unusual is the possibility of a disorder-induced Mott insulator-to-metal transition. The text was submitted by the authors in English.     

Quantum phase transitions in the bosonic single-impurity Anderson model

We consider a quantum impurity model in which a bosonic impurity level is coupled to a non-interacting bosonic bath, with the bosons at the impurity site subject to a local Coulomb repulsion U. Numerical renormalization group calculations for this bosonic single-impurity Anderson model reveal a zero-temperature phase diagram where Mott phases with reduced charge fluctuations are separated from a Bose-Einstein condensed phase by lines of quantum critical points. We discuss possible realizations of this model, such as atomic quantum dots in optical lattices. Furthermore, the bosonic single-impurity Anderson model appears as an effective impurity model in a dynamical mean-field theory of the Bose-Hubbard model.     

Role of the d-f Coulomb interaction in intermediate valence and Kondo systems: a numerical renormalization group study

Using the numerical renormalization group method, the dependences on temperature of the magnetic susceptibility χ(T) and specific heat C(T) are obtained for the single-impurity Anderson model with inclusion of d-f the Coulomb interaction. It is shown that the exciton effects caused by this effect (charge fluctuations) can significantly change the behaviour of C(T) in comparison with the standard Anderson model at moderately low temperatures, whereas the behaviour of χ(T) remains nearly universal. The ground-state and temperature-dependent renormalizations of the effective hybridization parameter and f-level position caused by the d-f interaction are calculated, and satisfactory agreement with the Hartree-Fock approximation is derived.     

Two-dimensional Anderson-Hubbard model in the DMFT + Σ approximation

The density of states, the dynamic (optical) conductivity, and the phase diagram of the paramagnetic two-dimensional Anderson-Hubbard model with strong correlations and disorder are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are accounted by the DMFT, while disorder is taken into account via the appropriate generalization of the self-consistent theory of localization. We consider the two-dimensional system with the rectangular “bare” density of states (DOS). The DMFT effective single-impurity problem is solved by numerical renormalization group (NRG). The “correlated metal,” Mott insulator, and correlated Anderson insulator phases are identified from the evolution of the density of states, optical conductivity, and localization length, demonstrating both Mott-Hubbard and Anderson metal-insulator transitions in two-dimensional systems of finite size, allowing us to construct the complete zero-temperature phase diagram of the paramagnetic Anderson-Hubbard model. The localization length in our approximation is practically independent of the strength of Hubbard correlations. But the divergence of the localization length in a finite-size two-dimensional system at small disorder signifies the existence of an effective Anderson transition.     

ON LOCALIZATION IN DISORDERED ELECTRON SYSTEMS

The field theory of Anderson localization of disordered electron systems is formulated in the framework of closed time path Green's functions (CTPGF). The properties of the mobility edge are studied by the renormalization group method and the density of states is found to be zero at the mobility edge.     

Variational numerical renormalization group: bridging the gap between NRG and density matrix renormalization group

The numerical renormalization group (NRG) is rephrased as a variational method with the cost function given by the sum of all the energies of the effective low-energy Hamiltonian. This allows us to systematically improve the spectrum obtained by NRG through sweeping. The ensuing algorithm has a lot of similarities to the density matrix renormalization group (DMRG) when targeting many states, and this synergy of NRG and DMRG combines the best of both worlds and extends their applicability. We illustrate this approach with simulations of a quantum spin chain and a single impurity Anderson model where the accuracy of the effective eigenstates is greatly enhanced as compared to the NRG, especially in the transition to the continuum limit.     

Kondo effect in a quantum dot coupled to ferromagnetic leads: a numerical renormalization group analysis

We investigate the effects of spin-polarized leads on the Kondo physics of a quantum dot using the numerical renormalization group method. Our study demonstrates in an unambiguous way that the Kondo effect is not necessarily suppressed by the lead polarization: While the Kondo effect is quenched for the asymmetric Anderson model, it survives even for finite polarizations in the regime where charge fluctuations are negligible. We propose the linear tunneling magnetoresistance as an experimental signature of these behaviors. We also report on the influence of spin-flip processes.     

Comparison between different computational schemes for variational calculations in nuclear structure

We compare several iteration methods for angular-momentum- and parity-projected Hartree-Fock calculations. We used the Anderson update, the modified Broyden method, newly introduced in nuclear-structure calculations, and variants of the Broyden-Fletcher-Goldhaber-Shanno methods (BFGS). We performed ground-state calculations for ¹⁸C and ⁶Li using the two-body Hamiltonian obtained from the CDBonn-2000 potential via the Lee-Suzuki renormalization method. We found that BFGS methods are superior to both the Anderson update and to the modified Broyden method. In the case of ⁶Li we found that the Anderson update and modified Broyden method do not converge to the angular-momentum- and parity-projected Hartree-Fock minimum. The reason is traced back to the lack of a mechanism that guarantees a decrease of the energy from one iteration to the next and to the fact that these methods guarantee a stationary solution rather than a minimum of the energy.     

Low-energy theory of disordered graphene

At low values of external doping, graphene displays a wealth of unconventional transport properties. Perhaps most strikingly, it supports a robust "metallic" regime, with universal conductance of the order of the conductance quantum. We here apply a combination of mean-field and bosonization methods to explore the large scale transport properties of the system. We find that, irrespective of the doping level, disordered graphene is subject to the common mechanisms of Anderson localization. However, at low doping a number of renormalization mechanisms conspire to protect the conductivity of the system, to an extend that strong localization may not be seen even at temperatures much smaller than those underlying present experimental work.     

Projective quantum monte carlo method for the anderson impurity model and its application to dynamical mean field theory

We develop a projective quantum Monte Carlo algorithm of the Hirsch-Fye type for obtaining ground state properties of the Anderson impurity model. This method is employed to solve the self-consistency equations of dynamical mean field theory. It is shown that the approach converges rapidly to the ground state so that reliable zero-temperature results are obtained. As a first application, we study the Mott-Hubbard metal-insulator transition of the frustrated one-band Hubbard model, reconfirming the numerical renormalization group results.     

Entanglement entropy in a one-dimensional disordered interacting system: the role of localization

The properties of the entanglement entropy (EE) in one-dimensional disordered interacting systems are studied. Anderson localization leaves a clear signature on the average EE, as it saturates on the length scale exceeding the localization length. This is verified by numerically calculating the EE for an ensemble of disordered realizations using the density matrix renormalization group method. A heuristic expression describing the dependence of the EE on the localization length, which takes into account finite-size effects, is proposed. This is used to extract the localization length as a function of the interaction strength. The localization length dependence on the interaction fits nicely with the expectations.     

Surprises in the phase diagram of an anderson impurity model for a single C60(n-) molecule

We find by Wilson numerical renormalization group and conformal field theory that a three-orbital Anderson impurity model for a C60(n-) molecule has a very rich phase diagram which includes non-Fermi-liquid stable and unstable fixed points with interesting properties, most notably high sensitivity to doping n. We discuss the implications of our results to the conductance behavior of C60-based single-molecule transistor devices.     

Spectral densities from dynamic density-matrix renormalization

Dynamic density-matrix renormalization provides valuable numerical information on dynamic correlations by computing convolutions of the corresponding spectral densities. Here we discuss and illustrate how and to which extent such data can be deconvolved to retrieve the wanted spectral densities. We advocate a nonlinear deconvolution scheme which minimizes the bias in the ansatz for the spectral density. The procedure is illustrated for the line shape and width of the Kondo peak (low energy feature) and for the line shape of the Hubbard satellites (high energy feature) of the single impurity Anderson model. It is found that the Hubbard satellites are strongly asymmetric.