Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory II

We present a shortened and simplified version of our proof \cite{Fischer:2006vf} of the uniqueness of the scaling solution for the infrared asymptotics of Green functions in Landau gauge Yang-Mills theory. The simplification relates to a new RG-invariant arrangement of Green functions applicable to general theories. As before the proof relies on the necessary consistency between Dyson-Schwinger equations (DSEs) and functional renormalisation group equations (FRGs). We also demonstrate the existence of a specific scaling solution for both, DSEs and FRGs, that displays uniform and soft kinematic singularities.Comment: 12 pages, 10 figure

Matrix product state approach for a two-lead, multi-level Anderson impurity model

We exploit the common mathematical structure of the numerical renormalization group and the density matrix renormalization group, namely, matrix product states, to implement an efficient numerical treatment of a two-lead, multi-level Anderson impurity model. By adopting a star-like geometry, where each species (spin and lead) of conduction electrons is described by its own Wilson chain, instead of using a single Wilson chain for all species together, we achieve a very significant reduction in the numerical resources required to obtain reliable results. We illustrate the power of this approach by calculating ground state properties of a four-level quantum dot coupled to two leads. The success of this proof-of-principle calculation suggests that the star geometry constitutes a promising strategy for future calculations the ground state properties of multi-band, multi-level quantum impurity models. Moreover, we show that it is possible to find an "optimal" chain basis, obtained via a unitary transformation (acting only on the index distinguishing different Wilson chains), in which degrees of freedom on different Wilson chains become effectively decoupled from each other further out on the Wilson chains. This basis turns out to also diagonalize the model's chain-to-chain scattering matrix. We demonstrate this for a spinless two-lead model, presenting DMRG-results for the mutual information between two sites located far apart on different Wilson chains, and NRG results with respect to the scattering matrix.Comment: extended version, 11 pages, 12 figure

The Mid-Pleistocene Transition induced by delayed feedback and bistability

The Mid-Pleistocene Transition, the shift from 41 kyr to 100 kyr glacial-interglacial cycles that occurred roughly 1 Myr ago, is often considered as a change in internal climate dynamics. Here we revisit the model of Quaternary climate dynamics that was proposed by Saltzman and Maasch (1988). We show that it is quantitatively similar to a scalar equation for the ice dynamics only when combining the remaining components into a single delayed feedback term. The delay is the sum of the internal times scales of ocean transport and ice sheet dynamics, which is on the order of 10 kyr. We find that, in the absence of astronomical forcing, the delayed feedback leads to bistable behaviour, where stable large-amplitude oscillations of ice volume and an equilibrium coexist over a large range of values for the delay. We then apply astronomical forcing. We perform a systematic study to show how the system response depends on the forcing amplitude. We find that over a wide range of forcing amplitudes the forcing leads to a switch from small-scale oscillations of 41 kyr to large-amplitude oscillations of roughly 100 kyr without any change of other parameters. The transition in the forced model consistently occurs near the time of the Mid-Pleistocene Transition as observed in data records. This provides evidence that the MPT could have been primarily a forcing-induced switch between attractors of the internal dynamics. Small additional random disturbances make the forcing-induced transition near 800 kyr BP even more robust. We also find that the forced system forgets its initial history during the small-scale oscillations, in particular, nearby initial conditions converge prior to transitioning. In contrast to this, in the regime of large-amplitude oscillations, the oscillation phase is very sensitive to random perturbations, which has a strong effect on the timing of the deglaciation events

Efficient simulation of infinite tree tensor network states on the Bethe lattice

We show that the simple update approach proposed by Jiang et. al. [H.C. Jiang, Z.Y. Weng, and T. Xiang, Phys. Rev. Lett. 101, 090603 (2008)] is an efficient and accurate method for determining the infinite tree tensor network states on the Bethe lattice. Ground state properties of the quantum transverse Ising model and the Heisenberg XXZ model on the Bethe lattice are studied. The transverse Ising model is found to undergo a second-order quantum phase transition with a diverging magnetic susceptibility but a finite correlation length which is upper-bounded by 1/ln(q-1) even at the transition point (q is the coordinate number of the Bethe lattice). An intuitive explanation on this peculiar "critical" phenomenon is given. The XXZ model on the Bethe lattice undergoes a first-order quantum phase transition at the isotropic point. Furthermore, the simple update scheme is found to be related with the Bethe approximation. Finally, by applying the simple update to various tree tensor clusters, we can obtain rather nice and scalable approximations for two-dimensional lattices.Comment: 9 pages, 10 figure

Matrix product state comparison of the numerical renormalization group and the variational formulation of the density matrix renormalization group

Wilson's numerical renormalization group (NRG) method for solving quantum impurity models yields a set of energy eigenstates that have the form of matrix product states (MPS). White's density matrix renormalization group (DMRG) for treating quantum lattice problems can likewise be reformulated in terms of MPS. Thus, the latter constitute a common algebraic structure for both approaches. We exploit this fact to compare the NRG approach for the single-impurity Anderson model to a variational matrix product state approach (VMPS), equivalent to single-site DMRG. For the latter, we use an ``unfolded'' Wilson chain, which brings about a significant reduction in numerical costs compared to those of NRG. We show that all NRG eigenstates (kept and discarded) can be reproduced using VMPS, and compare the difference in truncation criteria, sharp vs. smooth in energy space, of the two approaches. Finally, we demonstrate that NRG results can be improved upon systematically by performing a variational optimization in the space of variational matrix product states, using the states produced by NRG as input.Comment: 19 pages, 14 figure

SU(3) Anderson impurity model: A numerical renormalization group approach exploiting non-Abelian symmetries

We show how the density-matrix numerical renormalization group (DM-NRG) method can be used in combination with non-Abelian symmetries such as SU(N), where the decomposition of the direct product of two irreducible representations requires the use of a so-called outer multiplicity label. We apply this scheme to the SU(3) symmetrical Anderson model, for which we analyze the finite size spectrum, determine local fermionic, spin, superconducting, and trion spectral functions, and also compute the temperature dependence of the conductance. Our calculations reveal a rich Fermi liquid structure.Comment: 18 pages, 9 figure

Decoherence without dissipation?

In a recent article, Ford, Lewis and O'Connell (PRA 64, 032101 (2001)) discuss a thought experiment in which a Brownian particle is subjected to a double-slit measurement. Analyzing the decay of the emerging interference pattern, they derive a decoherence rate that is much faster than previous results and even persists in the limit of vanishing dissipation. This result is based on the definition of a certain attenuation factor, which they analyze for short times. In this note, we point out that this attenuation factor captures the physics of decoherence only for times larger than a certain time t_mix, which is the time it takes until the two emerging wave packets begin to overlap. Therefore, the strategy of Ford et al of extracting the decoherence time from the regime t < t_mix is in our opinion not meaningful. If one analyzes the attenuation factor for t > t_mix, one recovers familiar behaviour for the decoherence time; in particular, no decoherence is seen in the absence of dissipation. The latter conclusion is confirmed with a simple calculation of the off-diagonal elements of the reduced density matrix.Comment: 8 pages, 4 figure

Exploiting environmental resonances to enhance qubit quality factors

We discuss dephasing times for a two-level system (including bias) coupled to a damped harmonic oscillator. This system is realized in measurements on solid-state Josephson qubits. It can be mapped to a spin-boson model with a spectral function with an approximately Lorentzian resonance. We diagonalize the model by means of infinitesimal unitary transformations (flow equations), and calculate correlation functions, dephasing rates, and qubit quality factors. We find that these depend strongly on the environmental resonance frequency $\Omega$; in particular, quality factors can be enhanced significantly by tuning $\Omega$ to lie below the qubit frequency $\Delta$.Comment: 5 psges, 5 figure

Experimental evaluation of signal-to-noise in spectro-holography via modified uniformly redundant arrays in the soft x-ray and extreme ultraviolet spectral regime

We present dichroic x-ray lensless magnetic imaging by Fourier transform holography with an extended reference scheme via a modified uniformly redundant array (mURA). Holographic images of magnetic domains simultaneously generated by a single pinhole reference as well as by a mURA reference are compared with respect to the signal-to-noise ratio (SNR) as a function of exposure time. We apply this approach for spectro-holographic imaging of ferromagnetic domain patterns in Co/Pt multilayer films. Soft x-rays with wavelengths of 1.59 nm (Co L 3 absorption edge) and 20.8 nm (Co M 2,3 absorption edges) are used for image formation and to generate contrast via x-ray magnetic circular dichroism. For a given exposure time, the mURA-based holography allows to decouple the reconstruction SNR from the spatial resolution. For 1.59 nm wavelength, the reconstruction via the extended reference scheme shows no significant loss of spatial resolution compared to the single pinhole reference. In contrast, at 20.8 nm wavelength the single pinhole reveals some very intricate features which are lost in the image generated by the mURA, although overall a high-quality image is generated. The SNR-advantage of the mURA scheme is most notable when the hologram has to be encoded with few photons, while errors associated with the increased complexity of the reconstruction process reduce the advantage for high-photon-number experiments.BMBF, 05K13KT3, Verbundprojekt 05K2013 - DynaMaX: Messplatz für ultraschnelle Dynamik bei BESSY II. Teilprojekt