Simulation of Staggered Fermions by Polymer Algorithms

Abstract

The Pauli principle is usually implemented in the fermionic path integrals by Grassmann-variables. This form is, however, not well suited for a direct numerical simulation. The usual procedure is to perform the Grassmann-integral and simulate the bosonic system with an effective action containing the logarithm of the fermion determinant. Due to the non-locality of the effective bosonic action such fermion algorithms are, unfortunately, considerably slower than a typical pure bosonic algorithm (for a recent review see [1]). Moreover, the Monte Carlo integration of the effective bosonic field theory is only possible if the fermion determinant is positive. Examples where the fermion determinant is complex are, for instance: QCD with non-zero chemical potential or simple scalar-fermion models with chiral Yukawa-couplings etc. Under these circumtances the search for alternative, possibly local, fermion algorithms is well motivated.