Chiral symmetry and taste symmetry from the eigenvalue spectrum of staggered Dirac operators

  • We investigate general properties of the eigenvalue spectrum for improved staggered quarks. We introduce a new chirality operator [y5⊗1] and a new shift operator [1⊗ξ5], which respect the same recursion relation as the γ5 operator in the continuum. Then we show that matrix elements of the chirality operator sandwiched between two eigenstates of the staggered Dirac operator are related to those of the shift operator by the Ward identity of the conserved U (1)A symmetry of staggered fermion actions. We perform a numerical study in quenched QCD using HYP staggered quarks to demonstrate the Ward identity. We introduce a new concept of leakage patterns which collectively represent the matrix elements of the chirality operator and the shift operator sandwiched between two eigenstates of the staggered Dirac operator. The leakage pattern provides a new method to identify zero modes and nonzero modes in the Dirac eigenvalue spectrum. This method is as robust as the spectral flow method but requires much less computing power. Analysis using a machine learning technique confirms that the leakage pattern is universal, since the staggered Dirac eigenmodes on normal gauge configurations respect it. In addition, the leakage pattern can be used to determine a ratio of renormalization factors as a by-product. We conclude that it might be possible and realistic to measure the topological charge Q using the Atiya-Singer index theorem and the leakage pattern of the chirality operator in the staggered fermion formalism.

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Author:Hwancheol JeongORCiD, Chulwoo JungORCiD, Seungyeob Jwa, Jangho KimORCiD, Jeehun KimORCiD, Nam Soo KimORCiD, Sunghee Kim, Sunkyu Lee, Weonjong LeeORCiD, Youngjo Lee, Jeonghwan Pak
Parent Title (English):Physical review D
Place of publication:Woodbury, NY
Document Type:Article
Date of Publication (online):2021/07/26
Date of first Publication:2021/07/26
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Contributing Corporation:SWME Collaboration
Release Date:2022/07/11
Tag:Gauge theories; Lattice field theory
Issue:1, art. 4508
Article Number:4508
Page Number:30
First Page:1
Last Page:30
Funded by SCOAP. The research of W. Lee is supported by the Mid-Career Research Program (Grant No. NRF-2019R1A2C2085685) of the NRF grant funded by the Korean government (MOE). This work was supported by Seoul National University Research Grant No. 0409-20190221. W. Lee would like to acknowledge the support from the KISTI supercomputing center through the strategic support program for the supercomputing application research [No. KSC-2016-C3-0072, No. KSC-2017-G2-0009, No. KSC-2017-G2-0014, No. KSC-2018-G2-0004, No. KSC-2018-CHA-0010, No. KSC-2018-CHA-0043].
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Licence (German):License LogoCreative Commons - Namensnennung 4.0