Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2005-02-15
Comput.Phys.Commun.180:26-54,2009
Physics
High Energy Physics
High Energy Physics - Lattice
v2 60 pages; substantial changes to all parts of the article; v3 minor revsions
Scientific paper
10.1016/j.cpc.2008.08.006
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($\Delta\tau^2$) 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 $4^4$, $6^4$, and $8^4$ lattices at large masses.
Arnold Gabriele
Cundy Nigel
Frommer Andreas
Krieg Stefan
Lippert Th.
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