Time-evolving a matrix product state with long-ranged interactions

We introduce a numerical algorithm to simulate the time evolution of a matrix product state under a long-ranged Hamiltonian. In the effectively one-dimensional representation of a system by matrix product states, long-ranged interactions are necessary to simulate not just many physical interactions but also higher-dimensional problems with short-ranged interactions. Since our method overcomes the restriction to short-ranged Hamiltonians of most existing methods, it proves particularly useful for studying the dynamics of both power-law interacting one-dimensional systems, such as Coulombic and dipolar systems, and quasi two-dimensional systems, such as strips or cylinders. First, we benchmark the method by verifying a long-standing theoretical prediction for the dynamical correlation functions of the Haldane-Shastry model. Second, we simulate the time evolution of an expanding cloud of particles in the two-dimensional Bose-Hubbard model, a subject of several recent experiments.Comment: 5 pages + 3 pages appendices, 4 figure

Investigation of the coupling asymmetries at double-slit interference experiments

Double-slit experiments inferring the phase and the amplitude of the transmission coefficient performed at quantum dots (QD), in the Coulomb blockade regime, present anomalies at the phase changes depending on the number of electrons confined. This phase change cannot be explained if one neglects the electron-electron interactions. Here, we present our numerical results, which simulate the real sample geometry by solving the Poisson equation in 3D. The screened potential profile is used to obtain energy eigenstates and eigenvalues of the QD. We find that, certain energy levels are coupled to the leads stronger compared to others. Our results give strong support to the phenomenological models in the literature describing the charging of a QD and the abrupt phase changes.Comment: conference paper, 50th anniversary of Aharonov-Bohm effec

Level-occupation switching of the Quantum Dot, and phase anomalies in mesoscopic interferometry

For a variety of quantum dots, the widths of different single-particle levels may naturally differ by orders of magnitude. In particular, the width of one strongly coupled level may be larger than the spacing between other, very narrow, levels. We found that in this case many consecutive Coulomb blockade peaks are due to occupation of the same broad level. Between the peaks the electron jumps from this level to one of the narrow levels and the transmission through the dot at the next resonance essentially repeats that at the previous one. This offers a natural explanation of the salient features of the behavior of the transmission phase in an interferometer with a QD. The theory of this effect will be reviewed with special emphasis on the role of the interactions. New results on the dot-charging measurements and the fine structure of occupation switchings will be presented, accompanied by the unified description of the whole series of CB peaks caused by a single broad level. We then discuss the case where the system approaches the Kondo regime.Comment: 30 pages in IOP format, 11 figure

Josephson current through a single Anderson impurity coupled to BCS leads

We investigate the Josephson current J(\phi) through a quantum dot embedded between two superconductors showing a phase difference \phi. The system is modeled as a single Anderson impurity coupled to BCS leads, and the functional and the numerical renormalization group frameworks are employed to treat the local Coulomb interaction U. We reestablish the picture of a quantum phase transition occurring if the ratio between the Kondo temperature T_K and the superconducting energy gap \Delta or, at appropriate T_K/\Delta, the phase difference \phi or the impurity energy is varied. We present accurate zero- as well as finite-temperature T data for the current itself, thereby settling a dispute raised about its magnitude. For small to intermediate U and at T=0 the truncated functional renormalization group is demonstrated to produce reliable results without the need to implement demanding numerics. It thus provides a tool to extract characteristics from experimental current-voltage measurements.Comment: version accepted for publication in PR

A finite-frequency functional RG approach to the single impurity Anderson model

We use the Matsubara functional renormalization group (FRG) to describe electronic correlations within the single impurity Anderson model. In contrast to standard FRG calculations, we account for the frequency-dependence of the two-particle vertex in order to address finite-energy properties (e.g, spectral functions). By comparing with data obtained from the numerical renormalization group (NRG) framework, the FRG approximation is shown to work well for arbitrary parameters (particularly finite temperatures) provided that the electron-electron interaction U is not too large. We demonstrate that aspects of (large U) Kondo physics which are described well by a simpler frequency-independent truncation scheme are no longer captured by the 'higher-order' frequency-dependent approximation. In contrast, at small to intermediate U the results obtained by the more elaborate scheme agree better with NRG data. We suggest to parametrize the two-particle vertex not by three independent energy variables but by introducing three functions each of a single frequency. This considerably reduces the numerical effort to integrate the FRG flow equations.Comment: accepted by J. Phys.: Condensed Matte

Embedding method for the scattering phase in strongly correlated quantum dots

The embedding method for the calculation of the conductance through interacting systems connected to single channel leads is generalized to obtain the full complex transmission amplitude that completely characterizes the effective scattering matrix of the system at the Fermi energy. We calculate the transmission amplitude as a function of the gate potential for simple diamond-shaped lattice models of quantum dots with nearest neighbor interactions. In our simple models we do not generally observe an interaction dependent change in the number of zeroes or phase lapses that depend only on the symmetry properties of the underlying lattice. Strong correlations separate and reduce the widths of the resonant peaks while preserving the qualitative properites of the scattering phase.Comment: 11 pages, 3 figures. Proceedings of the Workshop on Advanced Many-Body and Statistical Methods in Mesoscopic Systems, Constanta, Romania, June 27th - July 2nd 2011. To appear in Journal of Physics: Conference Serie

Charge transport through single molecules, quantum dots, and quantum wires

We review recent progresses in the theoretical description of correlation and quantum fluctuation phenomena in charge transport through single molecules, quantum dots, and quantum wires. A variety of physical phenomena is addressed, relating to co-tunneling, pair-tunneling, adiabatic quantum pumping, charge and spin fluctuations, and inhomogeneous Luttinger liquids. We review theoretical many-body methods to treat correlation effects, quantum fluctuations, nonequilibrium physics, and the time evolution into the stationary state of complex nanoelectronic systems.Comment: 48 pages, 14 figures, Topical Review for Nanotechnolog

Interference effects in interacting quantum dots

In this paper we study the interplay between interference effects in quantum dots (manifested through the appearance of Fano resonances in the conductance), and interactions taken into account in the self-consistent Hartree-Fock approximation. In the non-interacting case we find that interference may lead to the observation of more than one conductance peak per dot level as a function of an applied gate voltage. This may explain recent experimental findings, which were thought to be caused by interaction effects. For the interacting case we find a wide variety of different interesting phenomena. These include both monotonous and non-monotonous filling of the dot levels as a function of an applied gate voltage, which may occur continuously or even discontinuously. In many cases a combination of the different effects can occur in the same sample. The behavior of the population influences, in turn, the conductance lineshape, causing broadening and asymmetry of narrow peaks, and determining whether there will be a zero transmission point. We elucidate the essential role of the interference between the dot levels in determining these outcomes. The effects of finite temperatures on the results are also examined.Comment: 11 pages, 9 fugures, REVTeX

Cognitive Effects of White Matter Pathology in Normal and Pathological Aging

We examined whether cerebrovascular white matter pathology is related to cognition as measured by the compound score of CERAD neuropsychological battery in cognitively normal older adults, patients with mild cognitive impairment, and patients with Alzheimer's disease (total n = 149), controlling for age and education. Trend-level effects of white matter pathology on cognition were only observed in patients with Alzheimer's disease (p = 0.062, eta(2) = 0.052), patients with severe frontal white matter pathology performed notably worse than those with milder pathology. This indicates that frontal cerebrovascular pathology may have an additive negative effect on cognition in Alzheimer's disease