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

Jeong, Hwancheol; Jung, Chulwoo; Jwa, Seungyeob; Kim, Jangho; Kim, Jeehun; Kim, Nam Soo; Kim, Sunghee; Lee, Sunkyu; Lee, Weonjong; Lee, Youngjo; Pak, Jeonghwan

doi:10.1103/physrevd.104.014508

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Staggered Dirac Eigenstate1

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2022

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“…Here, we adopt the same notation as in Ref. [4]. Staggered Dirac operator, 𝐷 𝑠 , is anti-Hermitian (𝐷 † 𝑠 = −𝐷 𝑠 ) and its eigenvalues are pure imaginary.…”

Section: Staggered Dirac Eigenstatementioning

confidence: 99%

Deep learning study on the Dirac eigenvalue spectrum of staggered quarks

Jeong¹,

Jung²,

Jwa³

et al. 2022

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We study the chirality of staggered quarks on the Dirac eigenvalue spectrum using deep learning (DL) techniques. The Kluberg-Stern method to construct staggered bilinear operators conserves continuum property such as recursion relations, uniqueness of chirality, and Ward identities, which leads to a unique and characteristic pattern (we call it "leakage pattern (LP)") in the matrix elements of the chirality operator sandwiched between two quark eigenstates of staggered Dirac operator. DL analysis gives 99.4(2)% accuracy on normal gauge configurations and 0.998 AUC (Area Under ROC Curve) for classifying non-zero mode octets in the Dirac eigenvalue spectrum. It confirms that the leakage pattern is universal on normal gauge configurations. The multi-layer perceptron (MLP) method turns out to be the best DL model for our study on the LP.

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“…Here, we adopt the same notation as in Ref. [4]. Staggered Dirac operator, 𝐷 𝑠 , is anti-Hermitian (𝐷 † 𝑠 = −𝐷 𝑠 ) and its eigenvalues are pure imaginary.…”

Section: Staggered Dirac Eigenstatementioning

confidence: 99%