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Staggered versus overlap fermions: a study in the Schwinger model with $N_f=0,1,2$

Stephan Dürr, Christian Hoelbling

TL;DR

This study compares staggered and overlap fermions in the 2D Schwinger model with ${N_f}=0,1,2$, using a $20\times20$ lattice at $\beta=4$ and spectrum-based reweighting to access dynamical flavors. It shows that naive staggered fermions yield qualitatively incorrect chiral behavior and topology near the chiral limit, whereas overlap fermions reproduce the known analytic results and the selection theorem for ${N_f}=1$, with topological observables aligning with continuum expectations. Importantly, applying one to three steps of APE/HYP smearing dramatically reduces lattice artefacts, enabling staggered results to converge toward the overlap predictions for moderate quark masses, though caveats remain in the chiral limit and at strong coupling. A spectral analysis suggests that smearing induces near-degenerate staggered modes that mimic the true zero-modes of overlap, offering a plausible mechanism for the observed improvements.

Abstract

We study the scalar condensate and the topological susceptibility for a continuous range of quark masses in the Schwinger model with $N_f=0,1,2$ dynamical flavors, using both the overlap and the staggered discretization. At finite lattice spacing the differences between the two formulations become rather dramatic near the chiral limit, but they get severely reduced, at the coupling considered, after a few smearing steps.

Staggered versus overlap fermions: a study in the Schwinger model with $N_f=0,1,2$

TL;DR

This study compares staggered and overlap fermions in the 2D Schwinger model with , using a lattice at and spectrum-based reweighting to access dynamical flavors. It shows that naive staggered fermions yield qualitatively incorrect chiral behavior and topology near the chiral limit, whereas overlap fermions reproduce the known analytic results and the selection theorem for , with topological observables aligning with continuum expectations. Importantly, applying one to three steps of APE/HYP smearing dramatically reduces lattice artefacts, enabling staggered results to converge toward the overlap predictions for moderate quark masses, though caveats remain in the chiral limit and at strong coupling. A spectral analysis suggests that smearing induces near-degenerate staggered modes that mimic the true zero-modes of overlap, offering a plausible mechanism for the observed improvements.

Abstract

We study the scalar condensate and the topological susceptibility for a continuous range of quark masses in the Schwinger model with dynamical flavors, using both the overlap and the staggered discretization. At finite lattice spacing the differences between the two formulations become rather dramatic near the chiral limit, but they get severely reduced, at the coupling considered, after a few smearing steps.

Paper Structure

This paper contains 6 sections, 26 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Scalar condensate
  3. Selection theorem
  4. Topological susceptibility
  5. Spectral hint
  6. Summary

Figures (7)

  • Figure 1: Scalar condensate after 0 (top) and 1 (bottom) steps of APE/HYP smearing.
  • Figure 2: Hybrid condensate after 0 (top) and 1 (bottom) steps of APE/HYP smearing.
  • Figure 3: Scalar condensate after 0 (top) and 3 (bottom) steps of APE/HYP smearing.
  • Figure 4: Sectoral condensate for overlap (top) and staggered quarks without smearing.
  • Figure 5: Sectoral condensate for staggered quarks with 1 and 3 steps of APE/HYP smearing.
  • ...and 2 more figures