Solving real time evolution problems by constructing excitation operators

In this paper we study the time evolution of an observable in the interacting fermion systems driven out of equilibrium. We present a method for solving the Heisenberg equations of motion by constructing excitation operators which are defined as the operators A satisfying [H,A]=\lambda A. It is demonstrated how an excitation operator and its excitation energy \lambda can be calculated. By an appropriate supposition of the form of A we turn the problem into the one of diagonalizing a series of matrices whose dimension depends linearly on the size of the system. We perform this method to calculate the evolution of the creation operator in a toy model Hamiltonian which is inspired by the Hubbard model and the nonequilibrium current through the single impurity Anderson model. This method is beyond the traditional perturbation theory in Keldysh-Green's function formalism, because the excitation energy \lambda is modified by the interaction and it will appear in the exponent in the function of time.Comment: 8 page

Tunneling exponents sensitive to impurity scattering in quantum wires

We show that the scaling exponent for tunneling into a quantum wire in the "Coulomb Tonks gas" regime of impenetrable, but otherwise free, electrons is affected by impurity scattering in the wire. The exponent for tunneling into such a wire thus depends on the conductance through the wire. This striking effect originates from a many-body scattering resonance reminiscent of the Kondo effect. The predicted anomalous scaling is stable against weak perturbations of the ideal Tonks gas limit at sufficiently high energies, similar to the phenomenology of a quantum critical point.Comment: 5 pages, 2 figures; slightly extended version of the published articl

The Crooks relation in optical spectra - universality in work distributions for weak local quenches

We show that work distributions and non-equilibrium work fluctuation theorems can be measured in optical spectra for a wide class of quantum systems. We consider systems where the absorption or emission of a photon corresponds to the sudden switch on or off of a local perturbation. For the particular case of a weak local perturbation, the Crooks relation establishes a universal relation in absorption as well as in emission spectra. Due to a direct relation between the spectra and work distribution functions this is equivalent to universal relations in work distributions for weak local quenches. As two concrete examples we treat the X-ray edge problem and the Kondo exciton.Comment: 4+ pages, 1 figure; version as publishe

Kondo resonance line-shape of magnetic adatoms on decoupling layers

The zero-bias resonance in the dI/dV tunneling spectrum recorded using a scanning tunneling microscope above a spin-1/2 magnetic adatom (such as Ti) adsorbed on a decoupling layer on metal surface can be accurately fitted using the universal spectral function of the Kondo impurity model both at zero field and at finite external magnetic field. Excellent agreement is found both for the asymptotic low-energy part and for the high-energy logarithmic tails of the Kondo resonance. For finite magnetic field, the nonlinear fitting procedure consists in repeatedly solving the impurity model for different Zeeman energies in order to obtain accurate spectral functions which are compared with the experimental dI/dV curves. The experimental results at zero field are sufficiently restraining to enable an unprecedented reliability in the determination of the Kondo temperature, while at finite fields the results are more ambiguous and two different interpretations are proposed

Entanglement of Two Impurities through Electron Scattering

We study how two magnetic impurities embedded in a solid can be entangled by an injected electron scattering between them and by subsequent measurement of the electron's state. We start by investigating an ideal case where only the electronic spin interacts successively through the same unitary operation with the spins of the two impurities. In this case, high (but not maximal) entanglement can be generated with a significant success probability. We then consider a more realistic description which includes both the forward and back scattering amplitudes. In this scenario, we obtain the entanglement between the impurities as a function of the interaction strength of the electron-impurity coupling. We find that our scheme allows us to entangle the impurities maximally with a significant probability

Magnetoconductance through a vibrating molecule in the Kondo regime

The effect of a magnetic field on the equilibrium spectral and transport properties of a single-molecule junction is studied using the numerical renormalization group method. The molecule is described by the Anderson-Holstein model in which a single vibrational mode is coupled to the electron density. The effect of an applied magnetic field on the conductance in the Kondo regime is qualitatively different in the weak and strong electron-phonon coupling regimes. In the former case, the Kondo resonance is split and the conductance is strongly suppressed by a magnetic field $g mu_B B \gtrsim k_BT_K$, with $T_K$ the Kondo temperature. In the strong electron-phonon coupling regime a charge analog of the Kondo effect develops. In this case the Kondo resonance is not split by the field and the conductance in the Kondo regime is enhanced in a broad range of values of $B$.Comment: 6 pages, 4 figure

Quantum phase transitions, frustration, and the Fermi surface in the Kondo lattice model

The quantum phase transition from a spin-Peierls phase with a small Fermi surface to a paramagnetic Luttinger-liquid phase with a large Fermi surface is studied in the framework of a one-dimensional Kondo-Heisenberg model that consists of an electron gas away from half filling, coupled to a spin-1/2 chain by Kondo interactions. The Kondo spins are further coupled to each other with isotropic nearest-neighbor and next-nearest-neighbor antiferromagnetic Heisenberg interactions which are tuned to the Majumdar-Ghosh point. Focusing on three-eighths filling and using the density-matrix renormalization-group (DMRG) method, we show that the zero-temperature transition between the phases with small and large Fermi momenta appears continuous, and involves a new intermediate phase where the Fermi surface is not well defined. The intermediate phase is spin gapped and has Kondo-spin correlations that show incommensurate modulations. Our results appear incompatible with the local picture for the quantum phase transition in heavy fermion compounds, which predicts an abrupt change in the size of the Fermi momentum.Comment: 9 pages, 8 figure

Numerical renormalization-group study of the Bose-Fermi Kondo model

We extend the numerical renormalization-group method to Bose-Fermi Kondo models (BFKMs), describing a local moment coupled to a conduction band and a dissipative bosonic bath. We apply the method to the Ising-symmetry BFKM with a bosonic bath spectral function $\eta(\omega)\propto \omega^s$, of interest in connection with heavy-fermion criticality. For $0<s<1$, an interacting critical point, characterized by hyperscaling of exponents and $\omega/T$-scaling, describes a quantum phase transition between Kondo-screened and localized phases. Connection is made to other results for the BFKM and the spin-boson model.Comment: 4 pages, 4 figure

Transport through quantum dots in mesoscopic circuits

We study the transport through a quantum dot, in the Kondo Coulomb blockade valley, embedded in a mesoscopic device with finite wires. The quantization of states in the circuit that hosts the quantum dot gives rise to finite size effects. These effects make the conductance sensitive to the ratio of the Kondo screening length to the wires length and provide a way of measuring the Kondo cloud. We present results obtained with the numerical renormalization group for a wide range of physically accessible parameters.Comment: 4 pages, 5 figure

Spectral properties of locally correlated electrons in a BCS superconductor

We present a detailed study of the spectral properties of a locally correlated site embedded in a BCS superconducting medium. To this end the Anderson impurity model with superconducting bath is analysed by numerical renormalisation group (NRG) calculations. We calculate one and two-particle dynamic response function to elucidate the spectral excitation and the nature of the ground state for different parameter regimes with and without particle-hole symmetry. The position and weight of the Andreev bound states is given for all relevant parameters. We also present phase diagrams for the different ground state parameter regimes. This work is also relevant for dynamical mean field theory extensions with superconducting symmetry breaking.Comment: 22 pages, 12 figure