2,602 research outputs found
General Algorithm For Improved Lattice Actions on Parallel Computing Architectures
Quantum field theories underlie all of our understanding of the fundamental
forces of nature. The are relatively few first principles approaches to the
study of quantum field theories [such as quantum chromodynamics (QCD) relevant
to the strong interaction] away from the perturbative (i.e., weak-coupling)
regime. Currently the most common method is the use of Monte Carlo methods on a
hypercubic space-time lattice. These methods consume enormous computing power
for large lattices and it is essential that increasingly efficient algorithms
be developed to perform standard tasks in these lattice calculations. Here we
present a general algorithm for QCD that allows one to put any planar improved
gluonic lattice action onto a parallel computing architecture. High performance
masks for specific actions (including non-planar actions) are also presented.
These algorithms have been successfully employed by us in a variety of lattice
QCD calculations using improved lattice actions on a 128 node Thinking Machines
CM-5.
{\underline{Keywords}}: quantum field theory; quantum chromodynamics;
improved actions; parallel computing algorithms
Tableau sequences, open diagrams, and Baxter families
Walks on Young's lattice of integer partitions encode many objects of
algebraic and combinatorial interest. Chen et al. established connections
between such walks and arc diagrams. We show that walks that start at
, end at a row shape, and only visit partitions of bounded height
are in bijection with a new type of arc diagram -- open diagrams. Remarkably
two subclasses of open diagrams are equinumerous with well known objects:
standard Young tableaux of bounded height, and Baxter permutations. We give an
explicit combinatorial bijection in the former case.Comment: 20 pages; Text overlap with arXiv:1411.6606. This is the full version
of that extended abstract. Conjectures from that work are proved in this wor
Nested quantum search and NP-complete problems
A quantum algorithm is known that solves an unstructured search problem in a
number of iterations of order , where is the dimension of the
search space, whereas any classical algorithm necessarily scales as . It
is shown here that an improved quantum search algorithm can be devised that
exploits the structure of a tree search problem by nesting this standard search
algorithm. The number of iterations required to find the solution of an average
instance of a constraint satisfaction problem scales as , with
a constant depending on the nesting depth and the problem
considered. When applying a single nesting level to a problem with constraints
of size 2 such as the graph coloring problem, this constant is
estimated to be around 0.62 for average instances of maximum difficulty. This
corresponds to a square-root speedup over a classical nested search algorithm,
of which our presented algorithm is the quantum counterpart.Comment: 18 pages RevTeX, 3 Postscript figure
Ab-initio study of the anomalies in the He atom scattering spectra of H/Mo(110) and H/W(110)
Helium atom scattering (HAS) studies of the H-covered Mo(110) and W(110)
surfaces reveal a twofold anomaly in the respective dispersion curves. In order
to explain this unusual behavior we performed density functional theory
calculations of the atomic and electronic structure, the vibrational
properties, and the spectrum of electron-hole excitations of those surfaces.
Our work provides evidence for hydrogen adsorption induced Fermi surface
nesting. The respective nesting vectors are in excellent agreement with the HAS
data and recent angle resolved photoemission experiments of the H-covered alloy
system Mo_0.95Re_0.05(110). Also, we investigated the electron-phonon coupling
and discovered that the Rayleigh phonon frequency is lowered for those critical
wave vectors. Moreover, the smaller indentation in the HAS spectra can be
clearly identified as a Kohn anomaly. Based on our results for the
susceptibility and the recently improved understanding of the He scattering
mechanism we argue that the larger anomalous dip is due to a direct interaction
of the He atoms with electron-hole excitations at the Fermi level.Comment: RevTeX, 32 pages, 17 figures, submitted to Phys. Rev.
Novel magnetic orderings in the kagome Kondo-lattice model
We consider the Kondo-lattice model on the kagome lattice and study its
weak-coupling instabilities at band filling fractions for which the Fermi
surface has singularities. These singularites include Dirac points, quadratic
Fermi points in contact with a flat band, and Van Hove saddle points. By
combining a controlled analytical approach with large-scale numerical
simulations, we demonstrate that the weak-coupling instabilities of the
Kondo-lattice model lead to exotic magnetic orderings. In particular, some of
these magnetic orderings produce a spontaneous quantum anomalous Hall state.Comment: 15 pages, 11 figure
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