The Mobius domain wall fermion algorithm

Abstract

We present a review of the properties of generalized domain wall Fermions, based on a (real) Möbius transformation on the Wilson overlap kernel, discussing their algorithmic efficiency, the degree of explicit chiral violations measured by the residual mass (m res ) and the Ward–Takahashi identities. The Möbius class interpolates between Shamir’s domain wall operator and Boriçi’s domain wall implementation of Neuberger’s overlap operator without increasing the number of Dirac applications per conjugate gradient iteration. A new scaling parameter (α) reduces chiral violations at finite fifth dimension (L s ) but yields exactly the same overlap action in the limit L s → ∞ . Through the use of 4d Red/Black preconditioning and optimal tuning for the scaling α(L s ), we show that chiral symmetry violations are typically reduced by an order of magnitude at fixed Ls . Here, we argue that the residual mass for a tuned Möbius algorithm with α = O(1/L s γ ) for γ < 1 will eventually fall asymptotically as m res = O(1/L s 1+γ ) in the case of a 5D Hamiltonian with out a spectral gap.