Ab initio study of the thermodynamics of quantum chromodynamics on the lattice at zero and finite densities

The WHOT-QCD Collaboration is pushing forward a series of lattice studies of quantum chromodynamics (QCD) at finite temperatures and densities using improved Wilson quarks. Because Wilson-type quarks require more computational resources than the more widely used staggeredtype quarks, various theoretical and computational techniques have to be developed and applied. In this paper, we introduce a fixed-scale approach armed with a T -integration method, a Gaussian method based on cumulant expansion, and a histogram method combined with the reweighting technique. Using these methods, we have carried out the first study of finite-density QCD with Wilson-type quarks and the first calculation of the equation of state with 2 + 1 flavors of Wilson-type quarks. We present the results of these studies and discuss perspectives towards clarification of the properties of 2 + 1 flavor QCD at the physical point at finite temperatures and densities.