A note on Zolotarev optimal rational approximation for the overlap Dirac operator

Abstract

We discuss the salient features of Zolotarev optimal rational approximation for the inverse square root function, in particular, for its applications in lattice QCD with overlap Dirac quark. The theoretical error bound for the matrix-vector multiplication $H_w(H_w^2{)}^{-1/2}Y$ is derived. We check that the error bound is always satisfied amply, for any QCD gauge configurations we have tested. An empirical formula for the error bound is determined, together with its numerical values (by evaluating elliptic functions) listed in Table 2 as well as plotted in Figure 3. Our results suggest that with Zolotarev approximation to $(H_w^2{)}^{-1/2}$, one can practically preserve the exact chiral symmetry of the overlap Dirac operator to very high precision, for any gauge configurations on a finite lattice.

23 pages, 5 eps figures, v2:minor clarifications, and references added, to appear in Phys. Rev. D

References in corpus (3)

• Numerical Methods for the QCD Overlap Operator: I. Sign-Function and Error Bounds
• Quenched chiral logarithms in lattice QCD with exact chiral symmetry
• Light quark masses in quenched QCD with exact chiral symmetry

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