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Research on the QCD phase diagram with lattice field theory methods isdominated by the use of rooted staggered fermions, as they are thecomputationally cheapest discretization available. We show that rootedstaggered fermions at a nonzero baryochemical potential $\mu_B$ predict a sharprise in the baryon density at low temperatures and $\mu_B \gtrsim 3 m_\pi/2$,where $m_\pi$ is the Goldstone pion mass. We elucidate the nature of thenon-analyticity behind this sharp rise in the density by a comparison ofreweighting results with a Taylor expansion of high order. While at first sightthis non-analytic behavior becomes apparent at the same position where the pioncondensation transition takes place in the phase-quenched theory, the nature ofthe non-analyticity in the two theories appears to be quite different: While atnonzero isospin density the data are consistent with a genuine thermodynamic(branch-point) singularity, the results at nonzero baryon density point to anessential singularity at $\mu_B=0$. The effect is absent for four flavors ofdegenerate quarks, where rooting is not used. For the two-flavor case, we shownumerical evidence that the magnitude of the effect diminishes on finerlattices. We discuss the implications of this technical complication on futurestudies of the QCD phase diagram.

Can rooted staggered fermions describe nonzero baryon density at low temperatures?