Systematic errors of Lüscher's fermion method and its extensions

Abstract

We study the systematic errors of Lüscher's formulation of dynamical Wilson quarks and some of its variants, in the weak and strong coupling limits, and on a sample of small configurations at finite β. We confirm the existence of an optimal window in the cutoff parameter ε, and the exponential decrease of the error with the number of boson families. A non-hermitian variant improves the approximation further and allows for an odd number of flavors. A simple and economical Metropolis test is proposed, which makes the algorithm exact.

Nonlinear realization of chiral symmetry on the lattice

“…A similar situation arises when one wants to simulate an odd number of flavors of Wilson fermions, for example, when one wants to include the strange quark in a QCD simulation. In this case -not directly addressing the potential sign problem -algorithms have been developed to perform numerical simulations [39][40][41][42]. It is to be expected that similar methods can be applied to the action presented here.…”

“…Fortunately, this sign problem is a lattice artifact which should disappear in the continuum limit, in particular, for sufficiently heavy fermions. Recently, without directly addressing the potential sign problem, dynamical fermion algorithms have been developed for an odd number of flavors of Wilson fermions [39][40][41][42]. We expect that similar methods are applicable to lattice fermions with nonlinearly realized chiral symmetry.…”

Nf = 1 QCD simulation with improved gauge action at finite temperature

“…This algorithm is considered to be an alternative one to simulate dynamical QCD. Boriçi and de Forcrand [3] noticed that the polynomial approximation can be used to simulate odd flavour QCD. Then the multiboson algorithm is used to study the deconfinement transition in one flavour QCD [4].…”

Simulation of nf = 3 QCD by Hybrid Monte Carlo

“…After invention of the multiboson algorithm, Boriçi and de Forcrand [5] noticed that a single det D can be treated in a manifestly positive way and an n f = 1 multiboson simulation was performed to study thermodynamics of n f = 1 QCD [6].…”

“…Originally he proposed it for two flavors QCD. Boriçi and de Forcrand [5] noticed that the determinant * Presented by T. Takaishi at LAT00. of a fermion matrix can be written in a manifestly positive way using a polynomial approximation, so that one can simulate odd flavors QCD with the multiboson method.…”