November 16, 2000
Similar papers 4
March 26, 1998
We discuss a number of lattice fermion actions solving the Ginsparg-Wilson relation. We also consider short ranged approximate solutions. In particular, we are interested in reducing the lattice artifacts, while avoiding (or suppressing) additive mass renormalization. In this context, we also arrive at a formulation of improved domain wall fermions.
October 23, 2002
This is an informal overview of methods and results on the QCD phase diagram and lattice termodynamics aimed at specialists in nearby fields.
October 16, 2003
I review the lattice formulations of vector-like gauge theories (e.g. QCD) with domain-wall/overlap fermions, and discuss how to optimize the chiral symmetry for any finite $ N_s $ (sites in the fifth dimension). In this formulation, quark propagators in gauge background can be computed efficiently through the effective 4D lattice Dirac operator.
March 31, 2022
We discuss algorithms for domain wall fermions focussing on accelerating Hybrid Monte Carlo sampling of gauge configurations. Firstly a new multigrid algorithm for domain wall solvers and secondly a domain decomposed hybrid monte carlo approach applied to large subvolumes and optimised for GPU accelerated nodes. We propose a formulation of DD-RHMC that is suitable for the simulation of odd numbers of fermions.
February 26, 2004
This paper reviews the most popular methods which are used in lattice QCD to compute the determinant of the lattice Dirac operator: Gaussian integral representation and noisy methods. Both of them lead naturally to matrix function problems. We review the most recent development in Krylov subspace evaluation of matrix functions. The second part of the paper reviews the formal relationship and algebraic structure of domain wall and overlap fermions. We review the multigrid algo...
April 18, 2012
We study QCD thermodynamics using two flavors of dynamical overlap fermions with quark masses corresponding to a pion mass of 350 MeV. We determine several observables on N_t=6 and 8 lattices. All our runs are performed with fixed global topology. Our results are compared with staggered ones and a nice agreement is found.
July 28, 2015
In 2+1 dimensions, Dirac fermions in reducible, i.e. four-component representations of the spinor algebra form the basis of many interesting model field theories and effective descriptions of condensed matter phenomena. This paper explores lattice formulations which preserve the global U(2N ) symmetry present in the massless limit, and its breakdown to U(N)xU(N) implemented by three independent and parity-invariant fermion mass terms. I set out generalisations of the Ginsparg...
March 18, 2017
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 formulat...
May 8, 2000
We define a sparse hermitian lattice Dirac matrix, $H$, coupling $2n+1$ Dirac fermions. When $2n$ fermions are integrated out the induced action for the last fermion is a rational approximation to the hermitian overlap Dirac operator. We provide rigorous bounds on the condition number of $H$ and compare them to bounds for the higher dimensional Dirac operator of domain wall fermions. Our main conclusion is that overlap fermions should be taken seriously as a practical alterna...
May 27, 1996
We perform a high statistics calculation of the equation of state for non-compact QED on large lattices. The calculation extends to fermionic correlation lengths of $\approx 8$, and it is combined with a finite size scaling analysis of the lattice data.