The Mobius domain wall fermion algorithm
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.
 Authors:

^{[1]};
^{[2]};
^{[3]}
 Boston Univ., Boston, MA (United States)
 Chamerstrasse, Zug (Switzerland)
 College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
 Publication Date:
 Report Number(s):
 JLABTHY121583; DOE/OR/231772232; arXiv:1206.5214
Journal ID: ISSN 00104655; PII: S001046551730036X; TRN: US1800951
 Grant/Contract Number:
 FG0207ER41527; FG0291ER40676; FC0206ER41440; AC0506OR23177; DGE0221680; PHY0427646; PHY0835713
 Type:
 Accepted Manuscript
 Journal Name:
 Computer Physics Communications
 Additional Journal Information:
 Journal Volume: 220; Journal Issue: C; Journal ID: ISSN 00104655
 Publisher:
 Elsevier
 Research Org:
 Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Lattice field theory
 OSTI Identifier:
 1416528
Brower, Richard C., Neff, Harmut, and Orginos, Kostas. The Mobius domain wall fermion algorithm. United States: N. p.,
Web. doi:10.1016/j.cpc.2017.01.024.
Brower, Richard C., Neff, Harmut, & Orginos, Kostas. The Mobius domain wall fermion algorithm. United States. doi:10.1016/j.cpc.2017.01.024.
Brower, Richard C., Neff, Harmut, and Orginos, Kostas. 2017.
"The Mobius domain wall fermion algorithm". United States.
doi:10.1016/j.cpc.2017.01.024. https://www.osti.gov/servlets/purl/1416528.
@article{osti_1416528,
title = {The Mobius domain wall fermion algorithm},
author = {Brower, Richard C. and Neff, Harmut and Orginos, Kostas},
abstractNote = {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 (mres) 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 (Ls) but yields exactly the same overlap action in the limit Ls → ∞ . Through the use of 4d Red/Black preconditioning and optimal tuning for the scaling α(Ls), 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/Lsγ) for γ < 1 will eventually fall asymptotically as mres = O(1/Ls1+γ) in the case of a 5D Hamiltonian with out a spectral gap.},
doi = {10.1016/j.cpc.2017.01.024},
journal = {Computer Physics Communications},
number = C,
volume = 220,
place = {United States},
year = {2017},
month = {7}
}