Hamiltonian lattice QCD at finite chemical potential

Details Hamiltonian lattice QCD at finite chemical potential Hamiltonian lattice QCD at finite chemical potential

1999-12-25

arxiv.org/abs/hep-lat/9912054v2

Phys.Rev. D62 (2000) 054508

Physics

High Energy Physics

High Energy Physics - Lattice

Final version appeared in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.62.054508

At sufficiently high temperature and density, quantum chromodynamics (QCD) is expected to undergo a phase transition from the confined phase to the quark-gluon plasma phase. In the Lagrangian lattice formulation the Monte Carlo 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 and in the strong coupling limit. At zero temperature, we calculate the vacuum energy, chiral condensate, quark number density and its susceptibility, as well as mass of the pseudoscalar, vector mesons and nucleon. We find that 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 $\mu_C \approx M_N^{(0)}/3$ (where $M_N^{(0)}$ is the nucleon mass at $\mu=0$).

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