We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in
the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in $N_f=2+1$ lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.
Hadronic matrix elements of proton decay are essential ingredients to bridge the grand unification theory to low energy observables like proton lifetime. In this paper we non-perturbatively calculate the matrix elements, relevant for the process of a
nucleon decaying into a pseudoscalar meson and an anti-lepton through generic baryon number violating four-fermi operators. Lattice QCD with 2+1 flavor dynamical domain-wall fermions with the {it direct} method, which is direct measurement of matrix element from three-point function without chiral perturbation theory, are used for this study to have good control over the lattice discretization error, operator renormalization, and chiral extrapolation. The relevant form factors for possible transition process from an initial proton or neutron to a final pion or kaon induced by all types of three quark operators are obtained through three-point functions of (nucleon)-(three-quark operator)-(meson) with physical kinematics. In this study all the relevant systematic uncertainties of the form factors are taken into account for the first time, and the total error is found to be the range 30%-40% for $pi$ and 20%-40% for $K$ final states.
We demonstrate the new class of variance reduction techniques for hadron propagator and nucleon isovector form factor in the realistic lattice of $N_f=2+1$ domain-wall fermion. All-mode averaging (AMA) is one of the powerful tools to reduce the stati
stical noise effectively for wider varieties of observables compared to existing techniques such as low-mode averaging (LMA). We adopt this technique to hadron two-point functions and three-point functions, and compare with LMA and traditional source-shift method in the same ensembles. We observe AMA is much more cost effective in reducing statistical error for these observables.
We propose a novel lattice calculation of spontaneous chiral symmetry breaking in QED model with 2+1 dimensional fermion brane. Considering the relativistic action with gauge symmetry we rigorously carry out path integral in Monte-Carlo simulation wi
th Fermi-velocity relevant to effective coupling constant. We numerically show the evidence of spontaneous chiral symmetry breaking in strong coupling region with chiral condensate, low-lying mode distribution and Nambu-Goldstone boson spectrum in bare Fermi-velocty $v=0.1$. This is a feasible study to investigate the phase structure of Graphene.
We propose a novel approach to the Graphene system using a local field theory of 4 dimensional QED model coupled to 2+1 dimensional Dirac fermions, whose velocity is much smaller than the speed of light. Performing hybrid Monte Carlo simulations of t
his model on the lattice, we compute the chiral condensate and its susceptibility with different coupling constant, velocity parameter and flavor number. We find that the chiral symmetry is dynamically broken in the small velocity regime and obtain a qualitatively consistent behavior with the prediction from Schwinger-Dyson equations.
We calculate the vacuum polarization functions on the lattice using the overlap fermion formulation.By matching the lattice data at large momentum scales with the perturbative expansion supplemented by Operator Product Expansion (OPE), we extract the
strong coupling constant $alpha_s(mu)$ in two-flavor QCD as $Lambda^{(2)}_{overline{MS}}$ = $0.234(9)(^{+16}_{- 0})$ GeV, where the errors are statistical and systematic, respectively. In addition, from the analysis of the difference between the vector and axial-vector channels, we obtain some of the four-quark condensates.
