958 research outputs found
Current status of Dynamical Overlap project
We discuss the adaptation of the Hybrid Monte Carlo algorithm to overlap
fermions. We derive a method which can be used to account for the delta
function in the fermionic force caused by the differential of the sign
function. We discuss the algoritmic difficulties that have been overcome, and
mention those that still need to be solved.Comment: Talk given at Workshop on Computational Hadron Physics, Nicosia,
September 2005. 8 page
Chiral symmetry breaking and topology for all N
We investigate spontaneous chiral symmetry breaking in SU(N) gauge theories
at large N using overlap fermions. The exact zero modes and the low-lying modes
of the Dirac operator provide the tools to gain insight into the interplay
between chiral symmetry breaking and topology. We find that topology indeed
drives chiral symmetry breaking at N=3 as well as at large N. By comparing the
results on various volumes and at different lattice spacings we are able to
show that our conclusions are not affected by finite volume effects and also
hold in the continuum limit. We then address the question whether the topology
can be usefully described in terms of instantons.Comment: Talk at Lattice 2003 (chiral); 3 pages, 2 figures, espcrc2.st
Improving the dynamical overlap algorithm
We present algorithmic improvements to the overlap Hybrid Monte Carlo
algorithm, including preconditioning techniques and improvements to the
correction step, used when one of the eigenvalues of the Kernel operator
changes sign, which is now O(\Delta t^2) exact.Comment: 6 pages, 3 figures; poster contribution at Lattice 2005(Algorithms
and machines
Dynamical overlap simulations using HMC
We apply the Hybrid Monte Carlo method to the simulation of overlap fermions.
We give the fermionic force for the molecular dynamics update. We present early
results on a small dynamical chiral ensemble.Comment: Lattice2004(machines), 3 pages; references updated, minor changes to
tex
Improving Inversions of the Overlap Operator
We present relaxation and preconditioning techniques which accelerate the
inversion of the overlap operator by a factor of four on small lattices, with
larger gains as the lattice size increases. These improvements can be used in
both propagator calculations and dynamical simulations.Comment: lattice2004(machines
Numerical Methods for the QCD Overlap Operator IV: Hybrid Monte Carlo
The extreme computational costs of calculating the sign of the Wilson matrix
within the overlap operator have so far prevented four dimensional dynamical
overlap simulations on realistic lattice sizes, because the computational power
required to invert the overlap operator, the time consuming part of the Hybrid
Monte Carlo algorithm, is too high. In this series of papers we introduced the
optimal approximation of the sign function and have been developing
preconditioning and relaxation techniques which reduce the time needed for the
inversion of the overlap operator by over a factor of four, bringing the
simulation of dynamical overlap fermions on medium-size lattices within the
range of Teraflop-computers.
In this paper we adapt the HMC algorithm to overlap fermions. We approximate
the matrix sign function using the Zolotarev rational approximation, treating
the smallest eigenvalues of the Wilson operator exactly within the fermionic
force. We then derive the fermionic force for the overlap operator, elaborating
on the problem of Dirac delta-function terms from zero crossings of eigenvalues
of the Wilson operator. The crossing scheme proposed shows energy violations
which are better than O() and thus are comparable with the
violations of the standard leapfrog algorithm over the course of a trajectory.
We explicitly prove that our algorithm satisfies reversibility and area
conservation. Finally, we test our algorithm on small , , and
lattices at large masses.Comment: v2 60 pages; substantial changes to all parts of the article; v3
minor revsion
- …