Computational methods for the fermion determinant and the link between overlap and domain wall fermions. (English) Zbl 1121.81328
Boriçi, Artan (ed.) et al., QCD and numerical analysis III. Proceedings of the third international workshop on numerical analysis and lattice QCD, Edinburgh, UK, June 30 – July 4, 2003. Berlin: Springer (ISBN 3-540-21257-4/pbk). Lecture Notes in Computational Science and Engineering 47, 25-39 (2005).
Summary: This paper reviews the most popular methods which are used in lattice quantum chromodynamics (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 algorithm to invert the overlap operator. It is described here as a preconditioned Jacobi iteration where the preconditioner is the Schur complement of a certain block of the truncated overlap matrix.
For the entire collection see [Zbl 1066.81001].
For the entire collection see [Zbl 1066.81001].
MSC:
| 81V05 | Strong interaction, including quantum chromodynamics |
| 82B10 | Quantum equilibrium statistical mechanics (general) |
| 81T25 | Quantum field theory on lattices |
| 81V70 | Many-body theory; quantum Hall effect |
