Abstract
The numerical properties of staggered Dirac operators with a taste-dependent mass term proposed by Adams [1, 2] and by Hoelbling [3] are compared with those of ordinary staggered and Wilson Dirac operators. In the free limit and on (quenched) interacting configurations, we consider their topological properties, their spectrum, and the resulting pion mass. Although we also consider the spectral structure, topological properties, locality, and computational cost of an overlap operator with a staggered kernel, we call attention to the possibility of using the Adams and Hoelbling operators without the overlap construction. In particular, the Hoelbling operator could be used to simulate two degenerate flavors without additive mass renormalization, and thus without fine-tuning in the chiral limit.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D.H. Adams, Theoretical foundation for the index theorem on the lattice with staggered fermions, Phys. Rev. Lett. 104 (2010) 141602 [arXiv:0912.2850] [INSPIRE].
D.H. Adams, Pairs of chiral quarks on the lattice from staggered fermions, Phys. Lett. B 699 (2011)394 [arXiv:1008.2833] [INSPIRE].
C. Hölbling, Single flavor staggered fermions, Phys. Lett. B 696 (2011) 422 [arXiv:1009.5362] [INSPIRE].
H.B. Nielsen and M. Ninomiya, No go theorem for regularizing chiral fermions, Phys. Lett. B 105 (1981)219 [INSPIRE].
H.B. Nielsen and M. Ninomiya, Absence of neutrinos on a lattice. 1. Proof by homotopy theory, Nucl. Phys. B 185 (1981) 20 [Erratum ibid. B 195 (1982) 541] [INSPIRE].
H.B. Nielsen and M. Ninomiya, Absence of neutrinos on a lattice. 2. Intuitive topological proof, Nucl. Phys. B 193 (1981) 173 [INSPIRE].
D. Friedan, A proof of the Nielsen-Ninomiya theorem, Commun. Math. Phys. 85 (1982) 481 [INSPIRE].
M. Lüscher, Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation, Phys. Lett. B 428 (1998) 342 [arXiv:hep-lat/9802011].
P.H. Ginsparg and K.G. Wilson, A remnant of chiral symmetry on the lattice, Phys. Rev. D 25 (1982)2649 [INSPIRE].
D.B. Kaplan, A method for simulating chiral fermions on the lattice, Phys. Lett. B 288 (1992)342 [hep-lat/9206013] [INSPIRE].
H. Neuberger, Exactly massless quarks on the lattice, Phys. Lett. B 417 (1998) 141 [hep-lat/9707022] [INSPIRE].
P. Hasenfratz, V. Laliena and F. Niedermayer, The index theorem in QCD with a finite cutoff, Phys. Lett. B 427 (1998) 125 [hep-lat/9801021] [INSPIRE].
K.G. Wilson, Quarks: from paradox to myth, in New phenomena in subnuclear physics, A. Zichichi ed., Plenum Press, New York U.S.A. (1977).
J.B. Kogut and L. Susskind, Hamiltonian Formulation of Wilson’s Lattice Gauge Theories, Phys. Rev. D 11 (1975) 395 [INSPIRE].
HPQCD Collaboration, UKQCD collaboration, E. Follana, A. Hart, C. Davies and Q. Mason, The Low-lying Dirac spectrum of staggered quarks, Phys. Rev. D 72 (2005) 054501 [hep-lat/0507011] [INSPIRE].
S. Dürr and C. Hölbling, Staggered versus overlap fermions: A Study in the Schwinger model with N(f )=0, 1, 2, Phys. Rev. D 69 (2004) 034503 [hep-lat/0311002] [INSPIRE].
S. Dürr, C. Hölbling and U. Wenger, Staggered eigenvalue mimicry, Phys. Rev. D 70 (2004) 094502 [hep-lat/0406027] [INSPIRE].
F. Bruckmann, S. Keppeler, M. Panero and T. Wettig, Polyakov loops and spectral properties of the staggered Dirac operator, Phys. Rev. D 78 (2008) 034503 [arXiv:0804.3929] [INSPIRE].
F. Bruckmann, S. Keppeler, M. Panero and T. Wettig, Polyakov loops and SU(2) staggered Dirac spectra, PoS LAT2007 (2007) 274 [arXiv:0802.0662] [INSPIRE].
M. Creutz, Comments on staggered fermions: Panel discussion, PoS CONFINEMENT8 (2008)016 [arXiv:0810.4526] [INSPIRE].
G.C. Donald, C.T. Davies, E. Follana and A.S. Kronfeld, Staggered fermions, zero modes and flavor-singlet mesons, Phys. Rev. D 84 (2011) 054504 [arXiv:1106.2412] [INSPIRE].
P. de Forcrand, A. Kurkela and M. Panero, Numerical properties of staggered overlap fermions, PoS LATTICE2010 (2010) 080 [arXiv:1102.1000] [INSPIRE].
P. de Forcrand, Overlap staggered fermions, http://super.bu.edu/~brower/qcdna6/talks/deforcrand.pdf.
L.H. Karsten, Lattice fermions in euclidean space-time, Phys. Lett. B 104 (1981) 315 [INSPIRE].
F. Wilczek, On lattice fermions, Phys. Rev. Lett. 59 (1987) 2397 [INSPIRE].
M. Creutz, Four-dimensional graphene and chiral fermions, JHEP 04 (2008) 017 [arXiv:0712.1201] [INSPIRE].
A. Boriçi, Creutz fermions on an orthogonal lattice, Phys. Rev. D 78 (2008) 074504 [arXiv:0712.4401] [INSPIRE].
S. Capitani, M. Creutz, J. Weber and H. Wittig, Renormalization of minimally doubled fermions, JHEP 09 (2010) 027 [arXiv:1006.2009] [INSPIRE].
M. Creutz, T. Kimura and T. Misumi, Index theorem and overlap formalism with naive and minimally doubled fermions, JHEP 12 (2010) 041 [arXiv:1011.0761] [INSPIRE].
T. Kimura, M. Creutz and T. Misumi, Index theorem and overlap formalism with naive and minimally doubled fermions, PoS LATTICE2011 (2011) 106 [arXiv:1110.2482] [INSPIRE].
T. Kimura, S. Komatsu, T. Misumi, T. Noumi, S. Torii, et al., Revisiting symmetries of lattice fermions via spin-flavor representation, JHEP 01 (2012) 048 [arXiv:1111.0402] [INSPIRE].
E. Follana, V. Azcoiti, G. Di Carlo and A. Vaquero, Spectral flow and index theorem for staggered fermions, PoS LATTICE2011 (2011) 100 [arXiv:1111.3502] [INSPIRE].
H. Sharatchandra, H. Thun and P. Weisz, Susskind fermions on a euclidean lattice, Nucl. Phys. B 192 (1981) 205 [INSPIRE].
F. Gliozzi, Spinor algebra of the one component lattice fermions, Nucl. Phys. B 204 (1982) 419 [INSPIRE].
C. van den Doel and J. Smit, Dynamical symmetry breaking in two flavor SU(N) and SO(N) lattice gauge theories, Nucl. Phys. B 228 (1983) 122 [INSPIRE].
H. Kluberg-Stern, A. Morel, O. Napoly and B. Petersson, Flavors of Lagrangian Susskind fermions, Nucl. Phys. B 220 (1983) 447 [INSPIRE].
M.F. Golterman and J. Smit, Selfenergy and flavor interpretation of staggered fermions, Nucl. Phys. B 245 (1984) 61 [INSPIRE].
P. de Forcrand, Simulating QCD at finite density, PoS LAT2009 (2009) 010 [arXiv:1005.0539] [INSPIRE].
D.H. Adams, Index and overlap construction for staggered fermions, PoS LATTICE2010 (2010)073 [arXiv:1103.6191] [INSPIRE].
P. de Forcrand, M. García Pérez, J. Hetrick, E. Laermann, J. Lagae and I. O. Stamatescu, Local topological and chiral properties of QCD, Nucl. Phys. Proc. Suppl. 73 (1999) 578 [hep-lat/9810033] [INSPIRE].
I. Horváth, Ginsparg-Wilson relation and ultralocality, Phys. Rev. Lett. 81 (1998) 4063 [hep-lat/9808002] [INSPIRE].
P. Hernández, K. Jansen and M. Lüscher, Locality properties of Neuberger’s lattice Dirac operator, Nucl. Phys. B 552 (1999) 363 [hep-lat/9808010] [INSPIRE].
W. Bietenholz, Optimised Dirac operators on the lattice: construction, properties and applications, Fortsch. Phys. 56 (2008) 107 [hep-lat/0611030] [INSPIRE].
S. Dürr and G. Koutsou, Brillouin improvement for Wilson fermions, Phys. Rev. D 83 (2011)114512 [arXiv:1012.3615] [INSPIRE].
A. Boriçi, On the Neuberger overlap operator, Phys. Lett. B 453 (1999) 46 [hep-lat/9810064] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1202.1867
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
de Forcrand, P., Kurkela, A. & Panero, M. Numerical properties of staggered quarks with a taste-dependent mass term. J. High Energ. Phys. 2012, 142 (2012). https://doi.org/10.1007/JHEP04(2012)142
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2012)142