Analytical contradictions of the fixed-node density matrix

Over the last decades the fixed-node method has been used for a numerical treatment of thermodynamic properties of strongly correlated Fermi systems. In this work correctness of the fixed-node method for ideal Fermi systems has been analytically analyzed. It is shown that the fixed-node prescription of calculation of the density matrix leads to contradictions even for two ideal fermions. The main conclusion of this work is that the fixed-node method can not reproduce the fermion density matrices and should be considered as uncontrolled empirical approach in treatment of thermodynamics of Fermi systems.