Chemical potential dependence of the endpoint of first-order phase transition in heavy-quark region of finite-temperature lattice QCD

We determine the location of the critical point where the first-order deconfining transition in the heavy-quark region turns into a crossover in finite-temperature and density lattice QCD with 2+1 flavors of Wilson quarks. Combining a hopping parameter expansion (HPE) of the quark determinant with a reweighting method, we evaluate the chemical potential dependence of the critical point. By systematically calculating the coefficients of the hopping parameter expansion up to a high order of HPE at finite chemical potential, we find that the higher order terms are strongly correlated with the Polyakov loop, which is the leading-order term, on each configuration. Moreover, their complex phases themselves, which are important at finite density, are also found to be strongly correlated with the complex phase of the Polyakov loop. Using this property, we develop a method for estimating the critical point incorporating high-order terms from calculations with only low-order terms. We report that the first-order phase transition region in the heavy-quark region becomes narrower exponentially with increasing the chemical potential. Since the hopping parameter of the critical point decreases exponentially as the density increases, the sign problem does not become serious even when the density increases, and critical points can be evaluated up to high densities.