Hamiltonian lattice quantum chromodynamics at finite chemical potential - art. no. 054508

At sufficiently high temperature and density, quantum chromodynamics (QCD) is expected to undergo a phase transition from the confined phase to the qu ark-gluon plasma phase. In the Lagrangian lattice formulation the Monte Car lo method works well for QCD at finite temperature; however, it breaks down at finite chemical potential. We develop a Hamiltonian approach to lattice QCD at finite chemical potential and solve it in the case of free quarks a nd in the strong coupling limit. At zero temperature, we calculate the vacu um energy, chiral condensate, quark number density and its susceptibility, as well as mass of the pseudoscalar, vector mesons and nucleon. We find tha t the chiral phase transition is of first order, and the critical chemical potential is mu(C) = m(dyn)((0)) (dynamical quark mass at mu = 0). This is consistent with mu(C) approximate to M-N((0))/3 (where M-N((0)) is the nucl eon mass at mu = 0).