TY  - JOUR
A1  - Jeong, Hwancheol
A1  - Jung, Chulwoo
A1  - Jwa, Seungyeob
A1  - Kim, Jangho
A1  - Kim, Jeehun
A1  - Kim, Nam Soo
A1  - Kim, Sunghee
A1  - Lee, Sunkyu
A1  - Lee, Weonjong
A1  - Lee, Youngjo
A1  - Pak, Jeonghwan
T1  - Chiral symmetry and taste symmetry from the eigenvalue spectrum of staggered Dirac operators
T2  - Physical review D
N2  - 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.
KW  - Gauge theories
KW  - Lattice field theory
Y1  - 2021
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/62956
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-629562
SN  - 2470-0029
N1  - 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].
VL  - 104.2021
IS  - 1, art. 4508
SP  - 1
EP  - 30
PB  - Inst.
CY  - Woodbury, NY
ER  -