Hamiltonian lattice quantum chromodynamics at finite chemical potential

Abstract

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 µ C = m (0) dyn (dynamical quark mass at µ = 0). This is consistent with µ C ≈ M (0) N /3 (where M (0) N is the nucleon mass at µ = 0). *

Recent Progress of Lattice QCD in China

“…The Hamiltonian formulation does not have such a problem and is therefore a promising alternative. Recently, we have developed a Hamiltonian approach to lattice QCD at finite density 9 . It avoids the usual problem in the Lagrangian Monte Carlo method of either an incorrect continuum limit or a premature onset of the transition to nonzero quark density as µ is raised.…”

Bound states and critical behavior of the Yukawa potential

“…Critical phenomena exist not only in Quantum Chromodynamics (QCD) at finite temperature/chemical potential [19,20,21,22], but also in the Yukawa potential in Quantum Mechanics (QM) [3,4,5,10,11,12,13]. For α = 0, the Yukawa potential reduces to the Coulomb potential, and it is known to have infinite number of bound states.…”

Chiral condensate thermal evolution at finite baryon chemical potential within chiral perturbation theory

“…On the theoretical side, first principle calculations on the quark-gluon phase performed on the lattice have been traditionally hindered by the well-known fermion determinant sign problem. The search for alternative approaches to overcome this problem, at least for some values of the chemical potential, have recently bolstered the activity in lattice QCD at finite density (see for example [1][2][3][4][5] for a review and further references). However, lattice studies still present some difficulties in the infinite volume extrapolation and most importantly in that they do not use realistic values for the quark and hadron masses, particularly the pions and kaons, which are the lightest mesons and the most abundant at low temperatures.…”