Staggered domain wall fermions

We construct domain wall fermions with a staggered kernel and investigate their spectral and chiral properties numerically in the Schwinger model. In some relevant cases we see an improvement of chirality by more than an order of magnitude as compared to usual domain wall fermions. Moreover, we present first results for four-dimensional quantum chromodynamics, where we also observe significant reductions of chiral symmetry violations for staggered domain wall fermions.Comment: 7 pages, 4 figures; v2: Added references; Proceedings for the 34th International Symposium on Lattice Field Theory, University of Southampton, UK, 24-30 July 201

Theoretical and Computational Aspects of New Lattice Fermion Formulations

In this work we investigate theoretical and computational aspects of novel lattice fermion formulations for the simulation of lattice gauge theories. The lattice approach to quantum gauge theories is an important tool for studying quantum chromodynamics, where it is the only known framework for calculating physical observables from first principles. In our investigations we focus on staggered Wilson fermions and the related staggered domain wall and staggered overlap formulations. Originally proposed by Adams, these new fermion discretizations bear the potential to reduce the computational costs of state-of-the-art Monte Carlo simulations. Staggered Wilson fermions combine aspects of both staggered and Wilson fermions while having a reduced number of fermion doublers compared to usual staggered fermions. Moreover, they can be used as a kernel operator for the domain wall fermion construction with potentially significantly improved chiral properties and for the overlap operator with its exact chiral symmetry. This allows the implementation of chirality on the lattice in a controlled manner at potentially significantly reduced costs. The practical potential and limitations of these new lattice fermions are also critically discussed.Comment: PhD thesis (Nanyang Technological University, 2016), 160 pages; includes unpublished results and extended discussions of studies previously presented in arXiv:1609.05114, arXiv:1602.08432, arXiv:1312.7230 and arXiv:1312.326

Characteristics of modern atmospheric dust deposition in snow on the Penny Ice Cap, Baffin Island, Arctic Canada

We evaluated the concentration, size and distribution of insoluble dust microparticles in snowpits on the Penny Ice Cap (PIC), Baffin Island, to define (1) the characteristics of modern atmospheric dust deposition at the site, (2) the relative contributions of proximal and distal dust sources, and (3) the effects of summer melting on depositional signals in snow. The mean concentration (143 mg kg−1), flux (4.8 mg cm2 yr−1) and diameter (2.3 mm) of dust deposited on the PIC are similar to those observed in remote Arctic sites such as central Greenland, implying that dust is primarily supplied through long-range transport from far-removed source regions (at least 102–103 km distant). There is evidence for two seasonal maxima of dust deposition, one in late winter-early spring and one in late summer-early fall, although seasonal signals can not always be resolved in the snowpack due to some post-depositional particle migration with summer melt. However, ice layers appear to limit the mobility of particles, thereby preserving valuable paleoclimatic information in the PIC ice core dust record at a multi-annual to decadal temporal resolution

Simple QED- and QCD-like Models at Finite Density

In this paper we discuss one-dimensional models reproducing some features of quantum electrodynamics and quantum chromodynamics at nonzero density and temperature. Since a severe sign problem makes a numerical treatment of QED and QCD at high density difficult, such models help to explore various effects peculiar to the full theory. Studying them gives insights into the large density behavior of the Polyakov loop by taking both bosonic and fermionic degrees of freedom into account, although in one dimension only the implementation of a global gauge symmetry is possible. For these models we evaluate the respective partition functions and discuss several observables as well as the Silver Blaze phenomenon.Comment: 5 pages, 2 figures. Final published versio

Computational efficiency of staggered Wilson fermions: A first look

Results on the computational efficiency of 2-flavor staggered Wilson fermions compared to usual Wilson fermions in a quenched lattice QCD simulation on $16^3\times32$ lattice at $\beta=6$ are reported. We compare the cost of inverting the Dirac matrix on a source by the conjugate gradient (CG) method for both of these fermion formulations, at the same pion masses, and without preconditioning. We find that the number of CG iterations required for convergence, averaged over the ensemble, is less by a factor of almost 2 for staggered Wilson fermions, with only a mild dependence on the pion mass. We also compute the condition number of the fermion matrix and find that it is less by a factor of 4 for staggered Wilson fermions. The cost per CG iteration, dominated by the cost of matrix-vector multiplication for the Dirac matrix, is known from previous work to be less by a factor 2-3 for staggered Wilson compared to usual Wilson fermions. Thus we conclude that staggered Wilson fermions are 4-6 times cheaper for inverting the Dirac matrix on a source in the quenched backgrounds of our study.Comment: v2: Major correction and revisions: we had overlooked a factor 1/4 in the cost estimate for matrix-vector multiplication with the staggered Wilson Dirac matrix. This gives an increased speed-up by a factor 4 for the overall computation cost. 7 pages, 3 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

Transformation-Dependent Performance-Enhancement of Digital Annealer for 3-SAT

Quadratic Unconstrained Binary Optimization (QUBO) problems are NP-hard problems and many real-world problems can be formulated as QUBO. Currently there are no algorithms known that can solve arbitrary instances of NP-hard problems efficiently. Therefore special-purpose hardware such as Digital Annealer, other Ising machines, as well as quantum annealers might lead to benefits in solving such problems. We study a particularly hard class of problems which can be formulated as QUBOs, namely Boolean satisfiability (SAT) problems, and specifically 3-SAT. One intriguing aspect about 3-SAT problems is that there are different transformations from 3-SAT to QUBO. We study the transformations' influence on the problem solution, using Digital Annealer as a special-purpose solver. Besides well-known transformations we investigate a novel in this context not yet discussed transformation, using less auxiliary variables and leading to very good performance. Using exact diagonalization, we explain the differences in performance originating from the different transformations. We envision that this knowledge allows for specifically engineering transformations that improve a solvers capacity to find high quality solutions. Furthermore, we show that the Digital Annealer outperforms a quantum annealer in solving hard 3-SAT instances.Comment: 10 pages, 4 figure