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We investigate a chiral property of the domain-wall fermion (DWF) system using the four-dimensional hermitian Wilson-Dirac operator $H_W$. A formula expressing the Ward-Takahashi identity quark mass $m_{5q}$ with eigenvalues of this operator is derived, which well explains the $N_5$ dependence of $m_{5q}$ observed in previous numerical simulations. We further discuss the chiral property of DWF in the large volume in terms of the spectra of $H_W$.
Chiral properties of QCD formulated with the domain-wall fermion (DWQCD) are studied using the anomalous quark mass m_{5q} and the spectrum of the 4-dimensional Wilson-Dirac operator. Numerical simulations are made with the standard plaquette gauge a
We calculate the spectral function of the QCD Dirac operator using the four-dimensional effective operator constructed from the Mobius domain-wall implementation. We utilize the eigenvalue filtering technique combined with the stochastic estimate of
The Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. The mathematical set-up for this theorem is, however, not directly related to the physical fermion system, as
In this paper, we present a method for the computation of the low-lying real eigenvalues of the Wilson-Dirac operator based on the Arnoldi algorithm. These eigenvalues contain information about several observables. We used them to calculate the sign