Peter Schmitteckert

Few-Photon Transport in Low-Dimensional Systems: Interaction-Induced Radiation Trapping

We present a detailed analysis of the dynamics of photon transport in waveguiding systems in the presence of a two-level system. In these systems, quantum interference effects generate a strong effective optical nonlinearity on the few-photon level. We clarify the relevant physical mechanisms through an appropriate quantum many-body approach. Based on this, we demonstrate that a single-particle photon-atom bound state with an energy outside the band can be excited via multiparticle scattering processes. We further show that these trapping effects are robust and, therefore, will be useful for the control of photon entanglement in solid-state based quantum-optical systems.

Nonequilibrium electron transport using the density matrix renormalization group method

We extended the Density Matrix Renormalization Group method to study the real time dynamics of interacting one dimensional spinless Fermi systems by applying the full time evolution operator to an initial state. As an example we describe the propagation of a density excitation in an interacting clean system and the transport through an interacting nano structure.

Twofold Advance in the Theoretical Understanding of Far-From-Equilibrium Properties of Interacting Nanostructures

We calculate the full I-V characteristics at vanishing temperature in the self-dual interacting resonant level model in two ways. The first uses careful time dependent density matrix renormalization group with a large number of states per block and a representation of the reservoirs as leads subjected to a chemical potential. The other is based on integrability in the continuum limit, and generalizes early work by Fendley, Ludwig, and Saleur on the boundary sine-Gordon model. The two approaches are in excellent agreement, and uncover among other things a power law decay of the current at large voltages when U>0.

DMRG evaluation of the Kubo formula —Conductance of strongly interacting quantum systems

In this paper we present a novel approach combining linear response theory (Kubo) for the conductance and the Density Matrix Renormalization Group (DMRG). The system considered is one-dimensional and consists of non-interacting tight-binding leads coupled to an interacting nanostructure via weak links. Electrons are treated as spinless fermions and two different correlation functions are used to evaluate the conductance. Exact diagonalization calculations in the non-interacting limit serve as a benchmark for our combined Kubo and DMRG approach in this limit. Including both weak and strong interaction we present DMRG results for an extended nanostructure consisting of seven sites. For the strongly interacting structure a simple explanation of the position of the resonances is given in terms of hard-core particles moving freely on a lattice of reduced size.

From the Fermi glass towards the Mott insulator in one dimension: Delocalization and strongly enhanced persistent currents

When a system of spinless fermions in a disordered mesoscopic ring becomes instable between the inhomogeneous configuration driven by the random potential (Anderson insulator) and the homogeneous one driven by repulsive interactions (Mott insulator), the persistent current can be enhanced by orders of magnitude. This is illustrated by a study of the change of the ground state energy under twisted boundary conditions using the density matrix renormalization group algorithm.

Anderson Localization versus Delocalization of Interacting Fermions in One Dimension

Using the density matrix renormalization group algorithm, we investigate the lattice model for spinless fermions in one dimension in the presence of a strong interaction and disorder. The phase sensitivity of the ground state energy is determined with high accuracy for systems up to a size of 60 lattice constants. This quantity is found to be log-normally distributed. The fluctuations grow algebraically with system size with a universal exponent of ~2/3 in the localized region of the phase diagram. Surprizingly, we find, for an attractive interaction, a delocalized phase of finite extension. The boundary of this delocalized phase is determined.

Strong enhancement of transport by interaction on contact links

Strong repulsive interactions within a one-dimensional Fermi system in a two-probe configuration normally lead to a reduced off-resonance conductance. We show that if the repulsive interaction extends to the contact regions, a strong increase of the conductance may occur, even for systems where one would expect to find a reduced conductance. An essential ingredient in our calculations is a momentum-space representation of the leads, which allows a high energy resolution. Furthermore, we demonstrate that these results are independent of the high-energy cutoff and that the relevant scale is set by the Fermi velocity.

Numerical renormalization group study of pseudo-fermion and slave-boson spectral functions in the single impurity Anderson model.

We use the numerical renormalization group to calculate the auxiliary spectral functions of the

Dynamics of photon transport through quantum impurities in dispersion-engineered one-dimensional systems

U=\infty

Tunneling spectra simulation of interacting Majorana wires

Anderson impurity model. The slave--boson and pseudo--fermion spectral functions diverge at the threshold with exponents