S. Andergassen

Interaction flow method for many-fermion systems

We propose an interaction flow scheme that sums up the perturbation expansion of many-particle systems by successively increasing the interaction strength. It combines the unbiasedness of renormalization group methods with the simplicity of straight-forward perturbation theory. Applying the scheme to fermions in one dimension and to the two-dimensional Hubbard model we find that at one-loop level and low temperatures there is ample agreement with previous one-loop renormalization group approaches. We furthermore present results for the momentum-dependence of spin, charge and pairing interactions in the two-dimensional Hubbard model.

Impurity and correlation effects on transport in one-dimensional quantum wires

We study transport through a one-dimensional quantum wire of correlated fermions connected to semi-infinite leads. The wire contains either a single impurity or two barriers, the latter allowing for resonant tunneling. In the leads the fermions are assumed to be non-interacting. The wire is described by a microscopic lattice model. Using the functional renormalization group we calculate the linear conductance for wires of mesoscopic length and for all relevant temperature scales. For a single impurity, either strong or weak, we find power-law behavior as a function of temperature. In addition, we can describe the complete crossover from the weak- to the strong-impurity limit. For two barriers, depending on the parameters of the enclosed quantum dot, we find temperature regimes in which the conductance follows power-laws with universal exponents as well as non-universal behavior. Our approach leads to a comprehensive picture of resonant tunneling. We compare our results with those of alternative approaches.

Correlation effects on resonant tunneling in one-dimensional quantum wires

We study resonant tunneling in a Luttinger liquid with a double barrier enclosing a dot region. Within a microscopic model calculation the conductance G as a function of temperature T is determined over several decades. We identify parameter regimes in which the peak value G_p(T) shows distinctive power-law behavior. For intermediate dot parameters G_p behaves in a non-universal way.

Functional renormalization group for Luttinger liquids with impurities

We improve the recently developed functional renormalization group (fRG) for impurities and boundaries in Luttinger liquids by including renormalization of the two-particle interaction, in addition to renormalization of the impurity potential. Explicit flow equations are derived for spinless lattice fermions with nearest neighbor interaction at zero temperature, and a fast algorithm for solving these equations for very large systems is presented. We compute spectral properties of single-particle excitations, and the oscillations in the density profile induced by impurities or boundaries for chains with up to 10 6 lattice sites. The expected asymptotic power-laws at low energy or long distance are fully captured by the fRG. Results on the relevant energy scales and crossover phenomena at intermediate scales are also obtained. A comparison with numerical density matrix renormalization results for systems with up to 1000 sites shows that the fRG with the inclusion of vertex renormalization is remarkably accurate even for intermediate interaction strengths.

Kondo physics in transport through a quantum dot with Luttinger liquid leads

We study the gate voltage dependence of the linear conductance through a quantum dot coupled to one-dimensional leads. For interacting dot electrons but noninteracting leads Kondo physics implies broad plateaulike resonances. In the opposite case Luttinger-liquid behavior leads to sharp resonances. In the presence of Kondo as well as Luttinger-liquid physics and for experimentally relevant parameters, we find a line shape that resembles the one of the Kondo case.

Renormalization group analysis of the one-dimensional extended Hubbard model with a single impurity

We analyze the one-dimensional extended Hubbard model with a single static impurity by using a computational technique based on the functional renormalization group. This extends previous work for spinless fermions to spin- 1 fermions. The underlying approximations are devised for weak interactions and arbitrary impurity strengths, and have been checked by comparing with density matrix renormalization group data. We present results for the density of states, the density profile and the linear conductance. Two-particle backscattering leads to striking effects, which are not captured if the bulk system is approximated by its low-energy fixed point, the Luttinger model. In particular, the expected decrease of spectral weight near the impurity and of the conductance at low energy scales is often preceded by a pronounced increase, and the asymptotic power laws are modified by logarithmic corrections.

Supercurrent through a multilevel quantum dot close to singlet-triplet degeneracy

We investigate two serially-aligned quantum dots in the molecular regime of large tunnel couplings t. A Zeeman field B is used to tune the energy difference of singlet and triplet spin configurations. Attaching this geometry to BCS source and drain leads with gap Delta and phase difference phi gives rise to an equilibrium supercurrent J. To compute J in presence of Coulomb interactions U between the dot electrons, we employ the functional renormalization group (FRG). For Bsimt -- where the singlet and lowest-lying triplet spin states are equal in energy -- the current exhibits characteristics of a 0-pi transition similar to a single impurity. Its magnitude in the pi phase, however, jumps discontinuously at B=t, being smaller on the triplet side. Exploiting the flexibility of the FRG, we demonstrate that this effect is generic and calculate J for realistic experimental parameters Delta, U, and gate voltages epsilon. To obtain a more thorough understanding of the discontinuity, we analytically treat the limit Delta=infty where one can access the exact many-particle states. Finally, carrying out perturbation theory in the dot-lead couplings substantiates the intuitive picture that Cooper pair tunneling is favored by a singlet spin configuration while inhibited by a triplet one.

A Gentle Introduction to the Functional Renormalization Group: The Kondo Effect in Quantum Dots

The functional renormalization group provides an efficient description of the interplay and competition of correlations on different energy scales in interacting Fermi systems. An exact hierarchy of flow equations yields the gradual evolution from a microscopic model Hamiltonian to the effective action as a function of a continuously decreasing energy cutoff. Practical implementations rely on suitable truncations of the hierarchy, which capture nonuniversal properties at higher energy scales in addition to the universal low-energy asymptotics. As a specific example we study transport properties through a single-level quantum dot coupled to Fermi liquid leads. In particular, we focus on the temperature T = 0 gate voltage dependence of the linear conductance. A comparison with exact results shows that the functional renormalization group approach captures the broad resonance plateau as well as the emergence of the Kondo scale. It can be easily extended to more complex setups of quantum dots.