Analytical contradictions of the 'fixed - node' density matrices

TL;DR

This paper analytically demonstrates that the widely used 'fixed-node method' for Fermi systems produces contradictions even in simple cases, questioning its reliability for thermodynamic calculations of strongly correlated fermions.

Contribution

It provides an analytical critique showing the 'fixed-node method' cannot accurately reproduce fermion density matrices, challenging its validity.

Findings

Contradictions arise in the 'fixed-node' method for ideal fermions.

The method cannot reproduce fermion density matrices accurately.

It should be regarded as an uncontrolled empirical approach.

Abstract

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.