Curious behavior of three-dimensional lattice Dirac operators coupled to a monopole background

Karthik, Nikhil; Narayanan, Rajamani

doi:10.1103/PhysRevD.100.094501

Title: Curious behavior of three-dimensional lattice Dirac operators coupled to a monopole background

Journal Article · Mon Nov 11 00:00:00 EST 2019 · Physical Review. D.

DOI:https://doi.org/10.1103/PhysRevD.100.094501· OSTI ID:1573868

Karthik, Nikhil;

We investigate numerically the effect of regulating fermions in the presence of singular background fields in three dimensions. For this, we couple free lattice fermions to a background compact U(1) gauge field consisting of a monopole-anti-monopole pair of magnetic charge ±Q separated by a distance s in a periodic L³ lattice, and study the low-lying eigenvalues of different lattice Dirac operators under a continuum limit defined by taking L → ∞ at fixed s/L. As the background gauge field is parity even, we look for a two-fold degeneracy of the Dirac spectrum that is expected of a continuum-like Dirac operator. The naive-Dirac operator exhibits such a parity-doubling, but breaks the degeneracy of the fermion-doubler modes for the Q lowest eigenvalues in the continuum limit. The Wilson-Dirac operator lifts the fermion-doublers but breaks the parity-doubling in the Q lowest modes even in the continuum limit. The overlap-Dirac operator shows parity-doubling of all the modes even at finite L that is devoid of fermion-doubling, and singles out as a properly regulated continuum Dirac operator in the presence of singular gauge field configurations albeit with a peculiar algorithmic issue.

View Journal Article

Cite

Export

Save

Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0012704

OSTI ID:: 1573868

Alternate ID(s):: OSTI ID: 1580268

Report Number(s):: BNL-212435-2019-JAAM; PRVDAQ; 094501

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Vol. 100 Journal Issue: 9; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (21)

From domain wall to overlap in 2 + 1 d Hands, Simon Physics Letters B, Vol. 754 https://doi.org/10.1016/j.physletb.2016.01.037	journal	March 2016
Magnetic monopole plasma phase in $(2 + 1) d$ compact quantum electrodynamics with fermionic matter Armour, Wesley; Hands, Simon; Kogut, John B. Physical Review D, Vol. 84, Issue 1 https://doi.org/10.1103/PhysRevD.84.014502	journal	July 2011
An accelerated conjugate gradient algorithm to compute low-lying eigenvalues — a study for the Dirac operator in SU(2) lattice QCD Kalkreuter, Thomas; Simma, Hubert Computer Physics Communications, Vol. 93, Issue 1 https://doi.org/10.1016/0010-4655(95)00126-3	journal	January 1996
Exactly massless quarks on the lattice Neuberger, Herbert Physics Letters B, Vol. 417, Issue 1-2 https://doi.org/10.1016/S0370-2693(97)01368-3	journal	January 1998
Comment on “’t Hooft vertices, partial quenching, and rooted staggered QCD” Creutz, Michael Physical Review D, Vol. 78, Issue 7 https://doi.org/10.1103/PhysRevD.78.078501	journal	October 2008
Monopole scaling dimension using Monte-Carlo simulation Karthik, Nikhil Physical Review D, Vol. 98, Issue 7 https://doi.org/10.1103/PhysRevD.98.074513	journal	October 2018
Hamiltonian formulation of Wilson's lattice gauge theories Kogut, John; Susskind, Leonard Physical Review D, Vol. 11, Issue 2 https://doi.org/10.1103/PhysRevD.11.395	journal	January 1975
Parity violation and gauge noninvariance of the effective gauge field action in three dimensions Redlich, A. N. Physical Review D, Vol. 29, Issue 10 https://doi.org/10.1103/PhysRevD.29.2366	journal	May 1984
Finite size effects and chiral symmetry breaking in quenched three-dimensional QED Hands, Simon; Kogut, John B. Nuclear Physics B, Vol. 335, Issue 2 https://doi.org/10.1016/0550-3213(90)90503-6	journal	May 1990
Phase of the fermion determinant in ${QED}_{3}$ using a gauge invariant lattice regularization Karthik, Nikhil; Narayanan, Rajamani Physical Review D, Vol. 92, Issue 2 https://doi.org/10.1103/PhysRevD.92.025003	journal	July 2015
Domain wall fermions for planar physics Hands, Simon Journal of High Energy Physics, Vol. 2015, Issue 9 https://doi.org/10.1007/JHEP09(2015)047	journal	September 2015
Parity anomaly and fermion-boson transmutation in 3-dimensional lattice QED Coste, A.; Lüscher, M. Nuclear Physics B, Vol. 323, Issue 3 https://doi.org/10.1016/0550-3213(89)90127-2	journal	September 1989
Quantum Chromodynamics on the Lattice Gattringer, Christof; Lang, Christian B. Lecture Notes in Physics https://doi.org/10.1007/978-3-642-01850-3	book	January 2010
Scale invariance of parity-invariant three-dimensional QED Karthik, Nikhil; Narayanan, Rajamani Physical Review D, Vol. 94, Issue 6 https://doi.org/10.1103/PhysRevD.94.065026	journal	September 2016
Axial-Anomaly-Induced Fermion Fractionization and Effective Gauge-Theory Actions in Odd-Dimensional Space-Times Niemi, A. J.; Semenoff, G. W. Physical Review Letters, Vol. 51, Issue 23 https://doi.org/10.1103/PhysRevLett.51.2077	journal	December 1983
Numerical methods for the QCDd overlap operator. I. Sign-function and error bounds van den Eshof, J.; Frommer, A.; Lippert, Th. Computer Physics Communications, Vol. 146, Issue 2 https://doi.org/10.1016/S0010-4655(02)00455-1	journal	July 2002
Study of chiral symmetry in quenched QCD using the overlap Dirac operator Edwards, Robert G.; Heller, Urs M.; Narayanan, Rajamani Physical Review D, Vol. 59, Issue 9 https://doi.org/10.1103/PhysRevD.59.094510	journal	April 1999
Flavor and topological current correlators in parity-invariant three-dimensional QED Karthik, Nikhil; Narayanan, Rajamani Physical Review D, Vol. 96, Issue 5 https://doi.org/10.1103/PhysRevD.96.054509	journal	September 2017
Magnetic Monopoles Shnir, Yakov M. https://doi.org/10.1007/3-540-29082-6	book	January 2005
No evidence for bilinear condensate in parity-invariant three-dimensional QED with massless fermions Karthik, Nikhil; Narayanan, Rajamani Physical Review D, Vol. 93, Issue 4 https://doi.org/10.1103/PhysRevD.93.045020	journal	February 2016
Note on the Zolotarev optimal rational approximation for the overlap Dirac operator Chiu, Ting-Wai; Hsieh, Tung-Han; Huang, Chao-Hsi Physical Review D, Vol. 66, Issue 11 https://doi.org/10.1103/PhysRevD.66.114502	journal	December 2002

Similar Records

Dislocations under gradient flow and their effect on the renormalized coupling

Journal Article · Fri Feb 12 00:00:00 EST 2021 · Physical Review. D. · OSTI ID:1573868

Hasenfratz, Anna; Witzel, Oliver

Fermionic field theory and gauge interactions on random lattices

Journal Article · Sat Oct 01 00:00:00 EDT 1994 · Annals of Physics (New York) · OSTI ID:1573868

Griffin, C J; Kieu, T D

Fermion doubling and gauge invariance on random lattices

Journal Article · Mon Jun 21 00:00:00 EDT 1993 · Physical Review Letters; (United States) · OSTI ID:1573868

Griffin, C J; Kieu, T D

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Title: Curious behavior of three-dimensional lattice Dirac operators coupled to a monopole background

Citation Formats

References (21)

Similar Records

Related Subjects