Staggered eigenvalue mimicry

TL;DR

The paper investigates whether UV-filtered staggered fermions can replicate the infrared spectrum of the overlap Dirac operator, thereby supporting the use of rooted staggered determinants in dynamical QCD. By comparing low-lying eigenvalues on dynamical and matched quenched lattices with varying smearing levels, the authors show that sufficient UV-filtering induces a fourfold near-degeneracy and a separation between would-be zero and nonzero modes, aligning with the overlap spectrum up to $O(a^2)$ effects and suggesting an approximate index theorem for filtered staggered fermions. They define and analyze pseudo-observables to probe degeneracy fuzziness, finding scaling compatible with $O(a^2)$ at strong filtering and finer lattices, and demonstrate that a UV-filtered overlap kernel is computationally cheaper. The results bolster the theoretical justification for rooted staggered approaches and hint at practical pathways to dynamical ${N_f}=2$ simulations using overlap or reweighting with UV-filtered determinants, potentially preserving topology and random-matrix universality while reducing cost.

Abstract

We study the infrared part of the spectrum for UV-filtered staggered Dirac operators and compare them to the overlap counterpart. With sufficient filtering and at small enough lattice spacing the staggered spectra manage to ``mimic'' the overlap version. They show a 4-fold near-degeneracy, and a clear separation between would-be zero modes and non-zero modes. This suggests an approximate index theorem for filtered staggered fermions and a correct sensitivity to the topology of QCD. Moreover, it supports square-rooting the staggered determinant to obtain dynamical ensembles with $N_f=2$.

Figures (8)

• Figure 1: Eigenvalues on the configurations 00 and 06 in the ensemble CU_0001.
• Figure 2: Eigenvalues on the configurations 14 and 26 in the ensemble CU_0001.
• Figure 3: Eigenvalues on the configuration 38 and 48 in the ensemble CU_0001.
• Figure 4: Staggered eigenvalues with/without relative normalization factor on the first one of our $6^4$ and $8^4$ lattices, compared to the corresponding overlap spectrum.
• Figure 5: Staggered eigenvalues with/without relative normalization factor on the first one of our $12^4, 16^4$ lattices, compared to the corresponding overlap spectrum.