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.Comment: 7 pages, 2 figures. Minor typos correcte

The Density Matrix Renormalization Group applied to single-particle Quantum Mechanics

A simplified version of White's Density Matrix Renormalization Group (DMRG) algorithm has been used to find the ground state of the free particle on a tight-binding lattice. We generalize this algorithm to treat the tight-binding particle in an arbitrary potential and to find excited states. We thereby solve a discretized version of the single-particle Schr\"odinger equation, which we can then take to the continuum limit. This allows us to obtain very accurate results for the lowest energy levels of the quantum harmonic oscillator, anharmonic oscillator and double-well potential. We compare the DMRG results thus obtained with those achieved by other methods.Comment: REVTEX file, 21 pages, 3 Tables, 4 eps Figure

Dynamical density-matrix renormalization-group method

I present a density-matrix renormalization-group (DMRG) method for calculating dynamical properties and excited states in low-dimensional lattice quantum many-body systems. The method is based on an exact variational principle for dynamical correlation functions and the excited states contributing to them. This dynamical DMRG is an alternate formulation of the correction vector DMRG but is both simpler and more accurate. The finite-size scaling of spectral functions is discussed and a method for analyzing the scaling of dense spectra is described. The key idea of the method is a size-dependent broadening of the spectrum.The dynamical DMRG and the finite-size scaling analysis are demonstrated on the optical conductivity of the one-dimensional Peierls-Hubbard model. Comparisons with analytical results show that the spectral functions of infinite systems can be reproduced almost exactly with these techniques. The optical conductivity of the Mott-Peierls insulator is investigated and it is shown that its spectrum is qualitatively different from the simple spectra observed in Peierls (band) insulators and one-dimensional Mott-Hubbard insulators.Comment: 16 pages (REVTEX 4.0), 10 figures (in 13 EPS files

Commensurate-incommensurate transition of cold atoms in an optical lattice

An atomic gas subject to a commensurate periodic potential generated by an optical lattice undergoes a superfluid--Mott insulator transition. Confining a strongly interacting gas to one dimension generates an instability where an arbitrary weak potential is sufficient to pin the atoms into the Mott state; here, we derive the corresponding phase diagram. The commensurate pinned state may be detected via its finite excitation gap and the Bragg peaks in the static structure factor.Comment: 4 pages, 2 figure

Density Matrices for a Chain of Oscillators

We consider chains with an optical phonon spectrum and study the reduced density matrices which occur in density-matrix renormalization group (DMRG) calculations. Both for one site and for half of the chain, these are found to be exponentials of bosonic operators. Their spectra, which are correspondingly exponential, are determined and discussed. The results for large systems are obtained from the relation to a two-dimensional Gaussian model.Comment: 15 pages,8 figure

First 10Gb/s Transmission with radiation-hardened Silicon Photonic Mach-Zehnder Modulators in a Full Transmission System

We present standard and radiation-hardened pn depletion-type Mach-Zehnder modulators (MZM) to be used in high-bandwidth, fully-integrated wavelength division multiplexing (WDM) transmitter designs, aiming to upgrade the optical data transmission of future detector systems. A detailed characterization of the modulators with respect to modulation efficiency and RF response was carried out. Based on this work, a first optical link with a data rate of 11.3 Gb/s was set up