Deep learning study on the Dirac eigenvalue spectrum of staggered quarks

TL;DR

This paper applies deep learning to analyze the Dirac eigenvalue spectrum of staggered quarks, revealing a universal leakage pattern in the chirality operator matrix elements with high accuracy and demonstrating the effectiveness of MLP models.

Contribution

It introduces a deep learning approach to identify universal patterns in the Dirac eigenvalue spectrum of staggered quarks, confirming the leakage pattern's universality.

Findings

Deep learning achieves 99.4% accuracy on gauge configurations.

DL classifies non-zero mode octets with 0.998 AUC.

MLP is the most effective model for this analysis.

Abstract

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.