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We report our recent studies on the zero temperature limit of Wilson fermion determinant at nonzero quark chemical potential. We show that the fermion determinant is independent of quark chemical potential and the quark number operator is zero for μ < mπ/2 in lattice QCD. A reduction formula of the fermion determinant, which is a formula to calculate the temporal part of the fermion determinant analytically, is a key to taking the zero temperature limit.

A property of fermions at finite density by a reduction formula of fermion determinant