Two-Flavor Lattice QCD with a Finite Density of Heavy Quarks: Heavy-Dense Limit and "Particle-Hole" Symmetry

We investigate the properties of the half-filling point in lattice QCD (LQCD), in particular the disappearance of the sign problem and the emergence of an apparent particle-hole symmetry, and try to understand where these properties come from by studying the heavy-dense fermion determinant and the corresponding strong-coupling partition function (which can be integrated analytically). We then add in a first step an effective Polyakov loop gauge action (which reproduces the leading terms in the character expansion of the Wilson gauge action) to the heavy-dense partition function and try to analyze how some of the properties of the half-filling point change when leaving the strong coupling limit. In a second step, we take also the leading nearest-neighbor fermion hopping terms into account (including gauge interactions in the fundamental representation) and mention how the method could be improved further to incorporate the full set of nearest-neighbor fermion hoppings. Using our mean-field method, we also obtain an approximate ($\mu$,T) phase diagram for heavy-dense LQCD at finite inverse gauge coupling $\beta$. Finally, we propose a simple criterion to identify the chemical potential beyond which lattice artifacts become dominant.