Perturbation expansion for 2-D Hubbard model

We develop an efficient method to calculate the third-order corrections to the self-energy of the hole-doped two-dimensional Hubbard model in space-time representation. Using the Dyson equation we evaluate the renormalized spectral function in various parts of the Brillouin zone and find significant modifications with respect to the second-order theory even for rather small values of the coupling constant U. The spectral function becomes unphysical for $U \simeq W$, where W is the half-width of the conduction band. Close to the Fermi surface and for U<W, the single-particle spectral weight is reduced in a finite energy interval around the Fermi energy. The increase of U opens a gap between the occupied and unoccupied parts of the spectral function.Comment: 17 pages, 11 Postscript figures, Phys. Rev. B, accepte

Electron correlation resonances in the transport through a single quantum level

Correlation effects in the transport properties of a single quantum level coupled to electron reservoirs are discussed theoretically using a non-equilibrium Green functions approach. Our method is based on the introduction of a second-order self-energy associated with the Coulomb interaction that consistently eliminates the pathologies found in previous perturbative calculations. We present results for the current-voltage characteristic illustrating the different correlation effects that may be found in this system, including the Kondo anomaly and Coulomb blockade. We finally discuss the experimental conditions for the simultaneous observation of these effects in an ultrasmall quantum dot.Comment: 4 pages (two columns), 3 figures under reques

The phase-dependent linear conductance of a superconducting quantum point contact

The exact expression for the phase-dependent linear conductance of a weakly damped superconducting quantum point contact is obtained. The calculation is performed by summing up the complete perturbative series in the coupling between the electrodes. The failure of any finite order perturbative expansion in the limit of small voltage and small quasi-particle damping is analyzed in detail. In the low transmission regime this nonperturbative calculation yields a result which is at variance with standard tunnel theory. Our result predicts the correct sign of the quasi-particle pair interference term and exhibits an unusual phase-dependence at low temperatures in qualitative agreement with the available experimental data.Comment: 12 pages (revtex) + 1 postscript figure. Submitted to Phys. Rev. Let

Universal features of electron-phonon interactions in atomic wires

The effect of electron-phonon interactions in the conductance through metallic atomic wires is theoretically analyzed. The proposed model allows to consider an atomic size region electrically and mechanically coupled to bulk electrodes. We show that under rather general conditions the features due to electron-phonon coupling are described by universal functions of the system transmission coefficients. It is predicted that the reduction of the conductance due to electron-phonon coupling which is observed close to perfect transmission should evolve into an enhancement at low transmission. This crossover can be understood in a transparent way as arising from the competition between elastic and inelastic processes.Comment: 5 pages, 5 figure

Andreev Level Qubit

We investigate the dynamics of a two-level Andreev bound state system in a transmissive quantum point contact embedded in an rf-SQUID. Coherent coupling of the Andreev levels to the circulating supercurrent allows manipulation and read out of the level states. The two-level Hamiltonian for the Andreev levels is derived, and the effect of interaction with the quantum fluctuations of the induced flux is studied. We also consider an inductive coupling of qubits, and discuss the relevant SQUID parameters for qubit operation and read out.Comment: 4 pages, 1 figur

Interpolating self-energy of the infinite-dimensional Hubbard model: Modifying the iterative perturbation theory

We develop an analytical expression for the self-energy of the infinite-dimensional Hubbard model that is correct in a number of different limits. The approach represents a generalization of the iterative perturbation theory to arbitrary fillings. In the weak-coupling regime perturbation theory to second order in the interaction U is recovered. The theory is exact in the atomic limit. The high-energy behavior of the self-energy up to order (1/E)**2 and thereby the first four moments of the spectral density are reproduced correctly. Referring to a standard strong-coupling moment method, we analyze the limit of strong U. Different modifications of the approach are discussed and tested by comparing with the results of an exact diagonalization study.Comment: LaTeX, 14 pages, 5 ps figures included, title changed, references updated, minor change

Investigation of the Two-Particle-Self-Consistent Theory for the Single-Impurity Anderson Model and an Extension to the Case of Strong Correlation

The two-particle-self-consistent theory is applied to the single-impurity Anderson model. It is found that it cannot reproduce the small energy scale in the strong correlation limit. A modified scheme to overcome this difficulty is proposed by introducing an appropriate vertex correction explicitly. Using the same vertex correction, the self-energy is investigated, and it is found that under certain assumptions it reproduces the result of the modified perturbation theory which interpolates the weak and the strong correlation limits.Comment: 5 pages, 7 figures, submitted to J. Phys. Soc. Jp

Iterated perturbation theory for the attractive Holstein and Hubbard models

A strictly truncated (weak-coupling) perturbation theory is applied to the attractive Holstein and Hubbard models in infinite dimensions. These results are qualified by comparison with essentially exact Monte Carlo results. The second order iterated perturbation theory is shown to be quite accurate in calculating transition temperatures for retarded interactions, but is not as accurate for the self energy or the irreducible vertex functions themselves. Iterated perturbation theory is carried out thru fourth order for the Hubbard model. The self energy is quite accurately reproduced by the theory, but the vertex functions are not. Anomalous behavior occurs near half filling because the iterated perturbation theory is not a conserving approximation. (REPLACED WITH UUENCODED FIGURES AT THE END. THE TEXT IS UNCHANGED)Comment: 27 pages, RevTex (figures appended at end

Two-level Hamiltonian of a superconducting quantum point contact

In a superconducting quantum point contact, dynamics of the superconducting phase is coupled to the transitions between the subgap states. We compute this coupling and derive the two-level Hamiltonian of the contact.Comment: REVTeX, 5 pages, reference adde

Subharmonic Shapiro steps and assisted tunneling in superconducting point contacts

We analyze the current in a superconducting point contact of arbitrary transmission in the presence of a microwave radiation. The interplay between the ac Josephson current and the microwave signal gives rise to Shapiro steps at voltages V = (m/n) \hbar \omega_r/2e, where n,m are integer numbers and \omega_r is the radiation frequency. The subharmonic steps (n different from 1) are a consequence of the ocurrence of multiple Andreev reflections (MAR) and provide an unambiguous signature of the peculiar ac Josephson effect at high transmission. Moreover, the dc current exhibits a rich subgap structure due to photon-assisted MARs.Comment: Revtex, 4 pages, 4 figure