QCD at Finite temperature and density with staggered and Wilson quarks

One of the most challenging issues in particle physics is to study QCD in extreme conditions. Precise determination of the QCD phase diagram on temperature $T$ and chemical potential $\mu$ plane will provide valuable information for quark-gluon plasma (QGP) and neutron star physics. We present results for phase structure on the $(\mu, T)$ plane for lattice QCD with Wilson fermions from strong coupling Hamiltonian analysis and Kogut-Susskind Fermions from Lagrangian Monte Carlo simulations at intermediate coupling.