Moebius Algorithm for Domain Wall and GapDW Fermions

TL;DR

The paper discusses the M"obius domain wall fermion algorithm, highlighting its performance benefits and equivalence to overlap fermions, especially at larger lattice spacings, with implications for lattice QCD simulations.

Contribution

It introduces the M"obius domain wall action as a generalization that reduces the separation needed for effective overlap fermions, improving computational efficiency in lattice QCD.

Findings

M"obius fermions reduce the required wall separation by over a factor of two.

The algorithm performs well with GapDWF at larger lattice spacings.

Exact equivalence of Ward-Takahashi identities in domain wall and overlap formulations.

Abstract

The M\"obius domain wall action \cite{Brower:2004xi} is a generalization of Shamir's action, which gives exactly the same overlap fermion lattice action as the separation ($L_s$) between the domain walls is taken to infinity. The performance advantages of the algorithm are presented for small ensembles of quenched, full QCD domain wall and Gap domain wall lattices \cite{Vranas:2006zk}. In particular, it is shown that at the larger lattice spacings relevant to current dynamical simulations M\"obius fermions work well together with GapDWF, reducing $L_s$ by more than a factor of two. It is noted that there is a precise map between the domain wall and effective overlap action at finite quark mass including finite $L_s$ chiral violations so that the Ward-Takahashi identities for the axial and vector currents are exactly equivalent in the two formulations.