Can rooted staggered fermions describe nonzero baryon density at low temperatures?
Szabolcs Borsányi (Department of Physics, Wuppertal University, Gaußstraße 20, D-42119, Wuppertal, Germany); Zoltán Fodor (Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52425 Jülich, Germany, Pennsylvania State University, Department of Physics, State College, Pennsylvania 16801, USA, Physics Department, UCSD, San Diego, California 92093, USA, Institute for Theoretical Physics, ELTE Eötvös Loránd University, Pázmány P. sétány 1/A, H-1117 Budapest, Hungary, Department of Physics, Wuppertal University, Gaußstraße 20, D-42119, Wuppertal, Germany); Matteo Giordano (Institute for Theoretical Physics, ELTE Eötvös Loránd University, Pázmány P. sétány 1/A, H-1117 Budapest, Hungary); Jana N. Guenther (Department of Physics, Wuppertal University, Gaußstraße 20, D-42119, Wuppertal, Germany); Sándor D. Katz (Institute for Theoretical Physics, ELTE Eötvös Loránd University, Pázmány P. sétány 1/A, H-1117 Budapest, Hungary); et al - Show all 7 authors
Research on the quantum chromodynamics (QCD) phase diagram with lattice field theory methods is dominated by the use of rooted staggered fermions, as they are the computationally cheapest discretization available. We show that rooted staggered fermions at a nonzero baryochemical potential predict a sharp rise in the baryon density at low temperatures and , where is the Goldstone pion mass. We elucidate the nature of the nonanalyticity behind this sharp rise in the density by a comparison of reweighting results with a Taylor expansion of high order. While at first sight this nonanalytic behavior becomes apparent at the same position where the pion condensation transition takes place in the phase-quenched theory, the nature of the nonanalyticity in the two theories appears to be quite different: While at nonzero isospin density the data are consistent with a genuine thermodynamic (branch-point) singularity, the results at nonzero baryon density point to an essential singularity at . The effect is absent for four flavors of degenerate quarks, where rooting is not used. For the two-flavor case, we show numerical evidence that the magnitude of the effect diminishes on finer lattices. We discuss the implications of this technical complication on future studies of the QCD phase diagram.
