Publications

Equilibrium Fermi-liquid coefficients for the fully screened N-channel Kondo model
Hanl, Markus, Weichselbaum, Andreas, von Delft, Jan and Kiselev, Mikhail
Phys. Rev. B , Volume 89,, page: 195131
2014

Abstract: We analytically and numerically compute three equilibrium Fermi-liquid coefficients of the fully screened N-channel Kondo model, namely c_B, c_T and c_\varepsilon, characterizing the magnetic field and temperature dependence of the resisitivity, and the curvature of the equilibrium Kondo resonance, respectively. We present a compact, unified derivation of the N-dependence of these coefficients, combining elements from various previous treatments of this model. We numerically compute these coefficients using the numerical renormalization group, with non-Abelian symmetries implemented explicitly, finding agreement with Fermi-liquid predictions on the order of 5% or better.

Low dimensionality of the surface conductivity of diamond
Hauf, Moritz V., Simon, Patrick, Seifert, Max, Holleitner, Alexander W., Stutzmann, Martin and Garrido, Jose A.
Phys. Rev. B , Volume 89, page: 115426
2014

Abstract: Undoped diamond, a remarkable bulk electrical insulator, exhibits a high surface conductivity in air when the surface is hydrogen terminated. Although theoretical models have claimed that a two-dimensional hole gas is established as a result of surface energy-band bending, no definitive experimental demonstration has been reported so far. Here, we prove the two-dimensional character of the surface conductivity by low-temperature characterization of diamond in-plane gated field-effect transistors that enable the lateral confinement of the transistor's drain-source channel to nanometer dimensions. In these devices, we observe Coulomb blockade effects of multiple quantum islands varying in size with the gate voltage. The charging energy and thus the size of these zero-dimensional islands exhibit a gate-voltage dependence which is the direct result of the two-dimensional character of the conductive channel formed at hydrogen-terminated diamond surfaces.

Far-from-equilibrium spin transport in Heisenberg quantum magnets
Hild, Sebastian, Fukuhara, Takeshi, Schauss, Peter, Zeiher, Johannes, Knap, Michael, Demler, Eugene, Bloch, Immanuel and Gross, Christian
2014

Abstract: We study experimentally the far-from-equilibrium dynamics in ferromagnetic Heisenberg quantum magnets realized with ultracold atoms in an optical lattice. After controlled imprinting of a spin spiral pattern with adjustable wave vector, we measure the decay of the initial spin correlations through single-site resolved detection. On the experimentally accessible timescale of several exchange times we find a profound dependence of the decay rate on the wave vector. In one-dimensional systems we observe diffusion-like spin transport with a dimensionless diffusion coefficient of 0.22(1). We show how this behavior emerges from the microscopic properties of the closed quantum system. In contrast to the one-dimensional case, our transport measurements for two-dimensional Heisenberg systems indicate anomalous super-diffusion.

Semicircle law for a matrix ensemble with dependent entries
Hochstättler, Winfried, Kirsch, Werner and Warzel, Simone
2014

Abstract: We study ensembles of random symmetric matrices whose entries exhibit certain correlations. Examples are distributions of Curie-Weiss-type. We provide a criterion on the correlations ensuring the validity of Wigner's semicircle law for the eigenvalue distribution measure. In case of Curie-Weiss distributions this criterion applies above the critical temperature (i.e. β<1). We also investigate the largest eigenvalue of certain ensembles of Curie-Weiss type and find a transition in its behavior at the critical temperature.

Determination of effective mechanical properties of a double-layer beam by means of a nano-electromechanical transducer
Hocke, Fredrik, Pernpeintner, Matthias, Zhou, Xiaoqing, Schliesser, Albert, J. Kippenberg, Tobias, Huebl, Hans and Gross, Rudolf
2014

Abstract: We investigate the mechanical properties of a doubly-clamped, double-layer nanobeam embedded into an electromechanical system. The nanobeam consists of a highly pre-stressed silicon nitride and a superconducting niobium layer. By measuring the mechanical displacement spectral density both in the linear and the nonlinear Duffing regime, we determine the pre-stress and the effective Young's modulus of the nanobeam. An analytical double-layer model quantitatively corroborates the measured values. This suggests that this model can be used to design mechanical multilayer systems for electro- and optomechanical devices, including materials controllable by external parameters such as piezoelectric, magnetrostrictive, or in more general multiferroic materials.

Sinkhorn normal form for unitary matrices
Idel, Martin and M. Wolf, Michael
2014

Abstract: Sinkhorn proved that every entry-wise positive matrix can be made doubly stochastic by multiplying with two diagonal matrices. In this note we prove a recently conjectured analogue for unitary matrices: every unitary can be decomposed into two diagonal unitaries and one whose row- and column sums are equal to one. The proof is non-constructive and based on a reformulation in terms of symplectic topology. As a corollary, we obtain a decomposition of unitary matrices into an interlaced product of unitary diagonal matrices and discrete Fourier transformations. This provides a new decomposition of linear optics arrays into phase shifters and canonical multiports described by Fourier transformations.

An invitation to trees of finite cone type: random and deterministic operators
Keller, Matthias, Lenz, Daniel and Warzel, Simone
2014

Abstract: Trees of finite cone type have appeared in various contexts. In particular, they come up as simplified models of regular tessellations of the hyperbolic plane. The spectral theory of the associated Laplacians can thus be seen as induced by geometry. Here we give an introduction focusing on background and then turn to recent results for (random) perturbations of trees of finite cone type and their spectral theory.

Controlling several atoms in a cavity
Keyl, Michael, Zeier, Robert and Schulte Herbrüggen, Thomas
New Journal of Physics , Volume 16(6), page: 065010
2014

Abstract: We treat control of several two-level atoms interacting with one mode of the electromagnetic field in a cavity. This provides a useful model to study pertinent aspects of quantum control in infinite dimensions via the emergence of infinite-dimensional system algebras. Hence we address problems arising with infinite-dimensional Lie algebras and those of unbounded operators. For the models considered, these problems can be solved by splitting the set of control Hamiltonians into two subsets: the first obeys an Abelian symmetry and can be treated in terms of infinite-dimensional Lie algebras and strongly closed subgroups of the unitary group of the system Hilbert space. The second breaks this symmetry, and its discussion introduces new arguments. Yet, full controllability can be achieved in a strong sense: e.g., in a time dependent Jaynes Cummings model we show that, by tuning coupling constants appropriately, every unitary of the coupled system (atoms and cavity) can be approximated with arbitrarily small error.

Ac-conductivity and electromagnetic energy absorption for the Anderson model in linear response theory
Klein, Abel and Müller, Peter
2014

Abstract: We continue our study of the ac-conductivity in linear response theory for the Anderson model using the conductivity measure. We establish further properties of the conductivity measure, including nontriviality at nonzero temperature, the high temperature limit, and asymptotics with respect to the disorder. We also calculate the electromagnetic energy absorption in linear response theory in terms of the conductivity measure.

Few-cycle, Broadband, Mid-infrared Optical Parametric Oscillator Pumped by a 20-fs Ti:sapphire Laser
Chaitanya Kumar, Suddapalli, Esteban-Martin, Adolfo, Ideguchi, Takuro, Yan, Ming, Holzner, Simon, W. Haensch, Theodor, Picque, Nathalie and Ebrahim-Zadeh, Majid
2014

Abstract: We report a few-cycle, broadband, singly-resonant optical parametric oscillator (OPO) for the mid-infrared based on MgO-doped periodically-poled LiNbO3 (MgO:PPLN), synchronously pumped by a 20-fs Ti:sapphire laser. By using crystal interaction lengths as short as 250 um, and careful dispersion management of input pump pulses and the OPO resonator, near-transform-limited, few-cycle idler pulses tunable across the mid-infrared have been generated, with as few as 3.7 optical cycles at 2682 nm. The OPO can be continuously tuned over 2179-3732 nm by cavity delay tuning, providing up to 33 mW of output power at 3723 nm. The idler spectra exhibit stable broadband profiles with bandwidths spaning over 422 nm (FWHM) recorded at 3732 nm. We investigate the effect of crystal length on spectral bandwidth and pulse duration at a fixed wavelength, confirming near-transform-limited idler pulses for all grating interaction lengths. By locking the repetition frequency of the pump laser to a radio-frequency reference, and without active stabilization of the OPO cavity length, an idler power stability better than 1.6% rms over >2.75 hours is obtained when operating at maximum output power, in excellent spatial beam quality with TEM00 mode profile.

Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet
Liu, Tao, Li, Wei, Weichselbaum, Andreas, von Delft, Jan and Su, Gang
2014

Abstract: We investigate the ground state properties of a spin-1 kagome antiferromagnetic Heisenberg (KAH) model using tensor-network methods. We find a trimerized ground state, with energy per site e_0\simeq-1.409 obtained by accurate calculations directly in the thermodynamic limit. The symmetry between left and right triangles is spontaneously broken, with a relative energy difference of δ ≈ 20%. The spin-spin, dimer-dimer, and chiral correlation functions are found to decay exponentially with a rather short correlation length, showing that the ground state is gapped. Based on this unambiguous numerical evidence, we identify the ground state of the spin-1 KAH model to be a simplex valence-bond crystal (SVBC). Besides the KAH model, we also discuss the spin-1 bilinear-biquadratic Heisenberg model on a kagome lattice, and determine its ground state phase diagram. In particular, we find a quantum phase transition between the SVBC and ferro-quadrupolar nematic states.

Algorithms for finite Projected Entangled Pair States
Lubasch, Michael, Ignacio Cirac, J. and Banuls, Mari-Carmen
Phys. Rev. B , Volume 90,, page: 064425
2014

Abstract: Projected Entangled Pair States (PEPS) are a promising ansatz for the study of strongly correlated quantum many-body systems in two dimensions. But due to their high computational cost, developing and improving PEPS algorithms is necessary to make the ansatz widely usable in practice. Here we analyze several algorithmic aspects of the method. On the one hand, we quantify the connection between the correlation length of the PEPS and the accuracy of its approximate contraction, and discuss how purifications can be used in the latter. On the other, we present algorithmic improvements for the update of the tensor that introduce drastic gains in the numerical conditioning and the efficiency of the algorithms. Finally, the state-of-the-art general PEPS code is benchmarked with the Heisenberg and quantum Ising models on lattices of up to 21 × 21 sites.

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