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We investigate the properties of the half-filling point in lattice QCD(LQCD), in particular the disappearance of the sign problem and the emergenceof an apparent particle-hole symmetry, and try to understand where theseproperties come from by studying the heavy-dense fermion determinant and thecorresponding strong-coupling partition function (which can be integratedanalytically). We then add in a first step an effective Polyakov loop gaugeaction (which reproduces the leading terms in the character expansion of theWilson gauge action) to the heavy-dense partition function and try to analyzehow some of the properties of the half-filling point change when leaving thestrong coupling limit. In a second step, we take also the leadingnearest-neighbor fermion hopping terms into account (including gaugeinteractions in the fundamental representation) and mention how the methodcould be improved further to incorporate the full set of nearest-neighborfermion 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 chemicalpotential beyond which lattice artifacts become dominant.

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