4,223 research outputs found
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 ; in particular, quality factors can be enhanced
significantly by tuning to lie below the qubit frequency .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
- …