Inversion Algorithms for Boriçi – Creutz fermions

¹ Faculty of Natural Sciences, University of Tirana, Bvd “Zog I”, Tiranë, Albania
² Polytechnic University of Tirana, Albania

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 15 April 2026

Abstract

In this work we present some inversion algorithms used for minimally doubled fermions and a comparative study of them in the case of a specific class of MDF: Boriçi - Creutz fermions. We have studied three main algorithms: Biconjugate gradient stabilized method BICGStab, the Conjugate Gradient method applied to the Normal Equations CGNE and Generalized minimal residual method GMRES, used for the inversion of the Dirac operator (BC operator in this case) and have seen how suitable are for non - hermitian operators, how fast they converge, the memory use and the preconditioning options. The tests are performed in the cluster of the Faculty of Natural Sciences, in a 64^4 lattice for five different mass quarks. The results show that the BICGStab algorithm converges faster than the other algorithm tested for Boriçi Creutz fermions, has a low memory use and turns to be one of the more efficient for MDF uses. In the chiral limit each one of them, presents specific challenges, but in the overall BICGStab algorithm seems to be better than the others, making it the default solver for BC fermions.