Dynamical fermion algorithms in numerical simulations

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Two-step multi-boson (TSMB) algorithm

The difficulty of numerical simulations with dynamical fermions comes, in general, from the non-locality of the effective lattice action for the bosonic (in case of QCD, the gluonic gauge-) fields. In the effective gauge action the logarithm of the determinant of the fermion matrix appears which becomes more and more non-local for fermions with small masses.

In case of the TSMB algorithm the fermion determinant is represented with the help of polynomial approximations. The TSMB algorithm was originally developed for numerical simulations in the supersymmetric Yang-Mills theory (for a review see hep-lat/0112007 ) but, after appropriate tuning, it can also be applied to QCD with light quarks. In the present version of TSMB several ideas on fermionic updating are incorporated: the local update step is based on Lüscher's multi-boson representation of the fermion determinant (hep-lat/9311007), the idea of a global correction step in the update (hep-lat/9505021), the final reweighting correction (hep-lat/9702016) and the determinant breakup boosting the performance (hep-lat/0203026).

Previous applications of TSMB are: supersymmetric Yang-Mills theory (SYM, MÜNSTER) and SU(2)-colour QCD with non-zero quark density (hep-lat/0006018 ). This algorithm can also be applied with more complicated fermion actions (hep-lat/0111015) including domain wall fermions (hep-lat/0204019).

Updating algorithms with multi-step stochastic correction

The two-step updating scheme of TSMB can be generalized to a multi-step scheme with nested multi-step stochastic correction (hep-lat/0506006 ). In the nested updating steps the fermion determinant is reproduced with increasing precision by appropriate polynomial approximations. In the first step, instead of multi-boson updating, one can also implement a Hybrid Monte Carlo (HMC) updating procedure, such as Polynomial Hybrid Monte Carlo (PHMC) (hep-lat/9702016 ).

Publication list

I. Montvay,
An algorithm for gluinos on the lattice,
Nucl. Phys. B466:259-284, (1996);   hep-lat/9510042

I. Montvay,
Quadratically optimized polynomials for fermion simulations,
Comput. Phys. Commun. 109:144-160, (1998);   hep-lat/9707005

R. Kirchner, S. Luckmann, I. Montvay, K. Spanderen, J. Westphalen,
Numerical simulation of dynamical gluinos: experience with a multi-bosonic algorithm and first results,
Nucl. Phys. Proc. Suppl. 73:828-833, (1999) 144;   hep-lat/9808024

I. Montvay,
Multi-bosonic algorithms for dynamical fermion simulations,
in Molecular Dynamics on Parallel Computers, Proceedings of the Workshop at NIC, Jülich, February 1999; edited by R. Esser, P. Grassberger, J. Grotendorst, M. Lewerenz; p.305;   hep-lat/9903029

I. Montvay,
Simulation of QCD and other similar theories,
Nucl. Phys. Proc. Suppl. 83:188-190, (2000);   hep-lat/9909020

I. Montvay,
Least-squares optimized polynomials for fermion simulations,
in Numerical Challenges in Lattice Quantum Chromodynamics, Proceedings of the Workshop in Wuppertal, August 1999; edited by A. Frommer, T. Lippert, B. Medeke, K. Schilling; Springer 2000, p. 153;   hep-lat/9911014

W. Schroers, N. Eicker, M. D'Elia, P. de Forcrand, C. Gebert, T. Lippert, I. Montvay, B. Orth, M. Pepe, K. Schilling,
The quest for light sea quarks: algorithms for the future,
Nucl. Phys. Proc. Suppl. 106:1082-1084, (2002);   hep-lat/0110033

I. Montvay,
Dynamical fermion algorithm for variable actions,
Phys. Lett. B527:155-160, (2002);   hep-lat/0111015

I.L. Bogolubsky, V.K. Mitrjushkin, I. Montvay, M. Muller-Preussker, N.V. Zverev,
Performance studies of the two-step multi-boson algorithm in compact lattice QED,
Nucl. Phys. Proc. Suppl. 106:1052-1054, (2002);   hep-lat/0111031

I. Montvay,
Unquenched domain wall quarks with multibosons,
Phys. Lett. B537:69-76, (2002);   hep-lat/0204019

I. Montvay,
Unquenched domain wall quarks with TSMB,
Nucl. Phys. Proc. Suppl. 119:843-845, (2003);   hep-lat/0208064

C. Gebert, I. Montvay,
A recurrence scheme for least-square optimized polynomials,

I. Montvay, E. Scholz,
Updating algorithms with multi-step stochastic correction,

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Last change on November 3, 2005