Resonant tunneling through quantum dot under a finite bias voltage at zero temperature is investigated by using the adaptive time-dependent density matrix renormalization group (TdDMRG) method. Quantum dot is modeled by the Anderson Hamiltonian with the one-dimensional nearest-neighbor tightbinding leads. Initially the ground state wave function is calculated with the usual DMRG method. Then the time evolution of the wave function due to the slowly changing bias voltage between the two leads is calculated by using the TdDMRG technique. Even though the system size is finite, the expectation values of current operator show steady-like behavior for a finite time interval, in which the system is expected to resemble the real nonequilibrium steady state of the infinitely long system. We show that from the time intervals one can obtain quantitatively correct results for differential conductance in a wide range of bias voltage. Finally we observe an anomalous behavior in the expectation value of the double occupation operator at the dot hn " n # i as a function of bias voltage.

A generalized Anderson model for a magnetic ion in a harmonic potential is formulated. The model is investigated by the numerical renormalization group (NRG) method. In addition to the conventional swave screening, the model exhibits phonon assisted p-wave Kondo effect as well as Yu and Anderson type Kondo effect. It is shown that the s-wave Kondo and the Yu-Anderson Kondo belong to the same fixed point. At the boundary between the s-wave and p-wave Kondo regions line of fixed points of the two channel Kondo effect is identified. Filled skutterudite compounds RT 4 X 12 (R = rare earth or alkaline earth element; T = Fe, Ru, Pt, or Os; X = P, As, Ge, or Sb) are characterized by their specific structures which involve a network of cages filled by guest ions. When the radius of the guest ion is smaller than the diameter of the cage, the guest ion vibrates with larger amplitude and smaller frequency than conventional localized modes. Such anharmonic local vibrations are referred to as rattling modes and may lead to novel phenomena of the coupled electron-phonon systems. Recent experiments on SmOs 4 Sb 12 show a large electronic specific heat coefficient linear in T, which is robust against magnetic field. 1) One possible scenario of the unusual behavior is the effect of strong electron-phonon coupling.When a magnetic ion couples with conduction electrons we expect Kondo effect due to the localized moment. On the other hand, it has been shown by Yu and Anderson (YA) that when conduction electrons couple strongly with ionic vibrations a different type of Kondo effect is expected.2) In this letter we will study the interplay between the conventional Kondo effect and the YA type one. Concerning the effects of coupling between a magnetic ion and ionic vibrations, Hotta has studied effects of anharmonicity in the Holstein-Anderson model.3) A lattice version of the Holstein-Anderson model is also studied. 4) In this letter, we will discuss effects of transverse vibrations on the Kondo effect rather than the breathing type vibrations.Suppose electron orbitals of a magnetic ion are described by the '-spherical-wave functions. Then the hybridization with the conduction electrons is given by overlap integrals between the '-wave localized orbitals and plane waves. To include the effect of vibrations the origin of the localized orbitals is shifted by Q which is the coordinate of the ion position. We can expand the overlap integral with respect to Q. In the zeroth order the localized '-spherical-waves hybridize with the '-partial-waves of conduction electrons. In the first order of Q, they hybridize with the ' þ 1 and ' À 1 partial waves. In the present letter we will concentrate on the simplest case of s-wave localized orbital. Then the total Hamiltonian up to the order of Q is given by the sum of

To discuss Kondo effects of a magnetic ion vibrating in the sea of conduction electrons, a generalized Anderson model is derived. The model includes a new channel of hybridization associated with phonon emission or absorption. In the simplest case of the localized electron orbital with the s-wave symmetry, hybridization with p-waves becomes possible. An interesting interplay among the conventional s-and p-wave Kondo effects and the Yu-Anderson-type Kondo effect is found, and the ground state phase diagram is determined by using the numerical renormalization group method. Two different types of stable fixed points are identified and the two-channel Kondo fixed points are generically realized at the boundary.

Nonlinear transport in the one dimensional Hubbard model at half-filling under a finite bias voltage is investigated by the adaptive time-dependent density matrix renormalization group method. For repulsive on-site interaction, dielectric breakdown of the Mott insulating ground state to a current-carrying nonequilibrium steady state is clearly observed when the voltage exceeds the charge gap. It is found that by increasing the voltage further the current-voltage characteristics are scaled only by the charge gap and the scaling curve exhibits almost linear dependence on the voltage whose slope is suppressed by the electron correlation. In the case of attractive interaction the linear conductance is the perfect one 2e 2 =h which agrees with the prediction by the Luttinger liquid theory. Emergence of rich variety of different states of matters is a consequence of electron-electron interaction. The Hubbard model is a prototypical interacting electron system and shows different phases depending on lattice structure, filling and interaction. When the band is half-filled and the Coulomb repulsion is sufficiently strong, the charge excitations involve a finite energy gap Á c , and this fact is a manifestation of the Mott insulating ground state. In one dimension (1-D) intriguing properties of the model including the Mott transition have been clarified by various analytic approaches: the Tomonaga-Luttinger liquid theory, the Bethe Ansatz and the conformal field theory.1) Therefore concerning equilibrium properties one can say that the 1-D Hubbard model is the best studied model in depth.Instead of chemical doping which is commonly used to realize metal-insulator transitions, one can also apply a bias voltage to break an insulating phase.2) This process, dielectric breakdown of a Mott insulator, may be called as a nonequilibrium metal-insulator transition. However, no systematic theoretical study on the breakdown of Mott insulators have been performed due to the difficulty to treat the nonequilibrium states of strongly correlated systems.Recently the adaptive time-dependent density matrix renormalization group (TdDMRG) algorithm was developed, 3) which is an extension of the DMRG 4) method to time-dependent problems. This technique has been used as a powerful numerical approach to nonequilibrium problems in one spatial dimension with strong correlation, such as single quantum dot system under finite bias voltages 5) and the interacting resonant level model. 6)Oka and Aoki utilized the TdDMRG method to study the breakdown of the Mott insulating phase of the 1-D Hubbard model driven by an external electric field. 7) They demonstrated that the phenomenological expression for the transition probability which is obtained by replacing the band gap in the Landau-Zener formula by the many-body charge gap Á c is consistent with the U dependence of the threshold electric field. They could discuss, however, only the threshold and it is necessary to investigate currentvoltage (I-V) characteristics beyond the breakdown to elucidate na...

This article is dedicated to Dieter Vollhardt on the occasion of his 60th birthday.Recent developments on studies of transport through quantum dots obtained by applying the time-dependent density matrix renormalization group method are summarized. Some new aspects of Kondo physics which appear in nonequilibrium steady states are discussed both for the single dot case and for the serially coupled double-quantum-dot case.