QCD phase diagram with 2-flavor lattice fermion formulations

We propose a new framework for investigating two-flavor lattice QCD with finite temperature and density. We consider the Karsten-Wilczek fermion formulation, in which a species-dependent imaginary chemical potential term can reduce the number of species to two without losing chiral symmetry. This lattice discretization is useful for study on finite-($T$,$\mu$) QCD since its discrete symmetries are appropriate for the case. To show its applicability, we study strong-coupling lattice QCD with temperature and chemical potential. We derive the effective potential of the scalar meson field and obtain a critical line of the chiral phase transition, which is qualitatively consistent with the phenomenologically expected phase diagram. We also discuss that $O(1/a)$ renormalization of imaginary chemical potential can be controlled by adjusting a parameter of a dimension-3 counterterm.