Mobius Fermions: Improved Domain Wall Chiral Fermions

TL;DR

This paper introduces a new class of domain wall fermions called Mobius fermions, which interpolate between existing forms and significantly reduce the computational resources needed for lattice QCD simulations while maintaining chiral symmetry.

Contribution

It defines Mobius fermions as a full Möbius transformation of the Wilson kernel, improving efficiency without increasing Dirac applications per iteration.

Findings

Reduced fifth dimension size by a factor of 2 or more

Maintained chiral symmetry violations at fixed residual mass

Demonstrated effectiveness on quenched Wilson lattices

Abstract

A new class of domain wall fermions is defined that interpolates between Shamir's and Bori\c{c}i's form without increasing the number of Dirac applications per CG iteration. This class represents a full (real) M\"obius transformation of the Wilson kernel. Simulations on quenched Wilson lattices with $\beta = 6.0$ show that the number of lattice sites ($L_s$) in the fifth dimension can be reduced by a factor of 2 or more at fixed value of chiral symmetry violations measured by the residual mass ($m_{res}$).