Center vortices in the novel phase of staggered fermions

The geometry of center vortices is studied in the novel lattice-artefact phase that appears with staggered fermions to elucidate any insight provided by the center-vortex degrees of freedom. For various numbers of fermion flavors, the single-site shift symmetry of the staggered-fermion action is broken in a finite region of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mo stretchy="false">(</a:mo><a:mi>β</a:mi><a:mo>,</a:mo><a:mi>m</a:mi><a:mo stretchy="false">)</a:mo></a:math> phase space. Simulations are performed with six degenerate fermion flavors and a range of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>β</e:mi></e:math> values that span the phase boundary. Center vortices are demonstrated to capture the broken shift symmetry that manifests in the unphysical phase. This persists at the level of each individual plaquette orientation, where it is revealed that only the plaquettes that span the broken dimension are affected. Several bulk center-vortex quantities, including the vortex and branching point densities, are considered to highlight other aspects of vortex geometry sensitive to the unphysical phase. A slight preference for the plaquettes affected by the broken shift symmetry to be pierced by a vortex is observed. This translates also to a greater branching point density in three-dimensional slices that span the broken dimension. Combined, these findings provide a novel characterization of the unphysical phase in terms of the fundamental center degrees of freedom.