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.

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.

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.

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. Surprisingly, we find, for an attractive interaction, a delocalized phase of finite extension. The boundary of this delocalized phase is determined.PACS numbers: 71.30.+h, 72.15.RnThe influence of electron-electron interaction on Anderson localization has attracted a lot of interest for several years. Many recent studies were motivated by the experimental observation of persistent currents in mesoscopic rings [1]. Motivated by an early suggestion [2] that the interaction between the electrons may give a significant contribution to the average persistent current, this phenomenon in the presence of both interaction and disorder has been investigated by various methods [3][4][5][6][7][8]. Nevertheless, the magnitude of the effect is still not well understood.In one dimension, interacting systems in the absence of disorder [9][10][11], as well as for disordered systems in the absence of interactions [12] are well studied. However, a clear understanding of the interplay between interaction and disorder has not yet been obtained. In this Letter, we present novel results of a detailed study of a simple interacting-fermion model with disorder. We determine the ground state phase sensitivity with high accuracy for a wide range of parameters and system sizes up to 60 lattice constants. Our main results are (i) a universal behavior of the rms-value of the logarithmic phase sensitivity, which grows with system size, M , proportional to M 2/3 in the localized region, and (ii) the zero-temperature phase diagram, which shows, for an attractive interaction a delocalized phase of finite extension.The numerical results are obtained with the density matrix renormalization group algorithm (DMRG) [13], which allows calculation of ground state properties of disordered, interacting fermion systems with an accuracy which is comparable to exact diagonalization, but for much larger systems [14,15]. In our implementation of the DMRG we perform 5 finite lattice sweeps keeping up to 750 states per block.We consider a chain of spinless fermions with nearestneighbor interaction and disorder,and twisted boundary conditions, c 0 = e iφ c M . The length of the chain is denoted by M , and the particle number is N . For simplicity, we will set t = 1 in some of the formulas below.The ground state energy E(φ) depends on the phase φ. The energy difference between periodic and anti-periodic boundary conditions, ∆E = (−), and the charge stiffness, D ∼ E ′′ (φ = 0), are a measure of the phase sensitivity of the system. In the clean limit, i.e. ǫ n = 0 for al...

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.c EDP Sciences

Numerical time evolution of transport states using time dependent Density Matrix Renormalization Group (td-DMRG) methods has turned out to be a powerful tool to calculate the linear and finite bias conductance of interacting impurity systems coupled to non-interacting one-dimensional leads. Several models, including the Interacting Resonant Level Model (IRLM), the Single Impurity Anderson Model (SIAM), as well as models with different multi site structures, have been subject of investigations in this context. In this work we give an overview of the different numerical approaches that have been successfully applied to the problem and go into considerable detail when we comment on the techniques that have been used to obtain the full I-V-characteristics for the IRLM. Using a model of spinless fermions consisting of an extended interacting nanostructure attached to non-interacting leads, we explain the method we use to obtain the current-voltage characteristics and discuss the finite size effects that have to be taken into account. We report results for the linear and finite bias conductance through a seven site structure with weak and strong nearest-neighbor interactions. Comparison with exact diagonalisation results in the non-interacting limit serve as a verification of the accuracy of our approach. Finally we discuss the possibility of effectively enlarging the finite system by applying damped boundaries and give an estimate of the effective system size and accuracy that can be expected in this case.

Recent tunneling experiments on InSb hybrid superconductor-semiconductor devices have provided hope for a stabilization of Majorana edge modes in a spin-orbit quantum wire subject to a magnetic field and superconducting proximity effect. Connecting the experimental scenario with a microscopic description poses challenges of different kind, such as accounting for the effect of interactions on the tunneling properties of the wire. We develop a density matrix renormalization group (DMRG) analysis of the tunneling spectra of interacting Majorana chains, which we explicate for the Kitaev chain model. Our DMRG approach allows us to calculate the spectral function down to zero frequency, where we analyze how the Majorana zero-bias peak is affected by interactions. From the study of topological phase transitions between the topological and trivial superconducting phase in the wire, we argue that the bulk gap closure generically affects both the proximity peaks and the Majorana peak, which should be observable in the transport signal.

We analyze the role of quantum interference effects induced by an embedded two-level system on the photon transport properties in waveguiding structures that exhibit cutoffs (band edges) in their dispersion relation. In particular, we demonstrate that these systems invariably exhibit single-particle photon-atom bound states and strong effective nonlinear responses on the few-photon level. Based on this, we find that the properties of these photon-atom bound states may be tuned via the underlying dispersion relation and that their occupation can be controlled via multiparticle scattering processes. This opens an interesting route for controlling photon transport properties in a number of solid-state-based quantum optical systems and the realization of corresponding functional elements and devices.