Positivity Preserving Density Matrix Minimization for Fermi-Dirac States at Finite Temperatures

Abstract

We present methods for calculating the Fermi-Dirac density matrix for electronic structure problems at finite temperature while preserving physicality by construction. These methods model cooling a state initially at infinite temperature down to the desired finite temperature. We consider both the grand canonical ensemble (constant chemical potential) and highlight subtleties involved with treating the canonical ensemble (constant number of electrons) that have been overlooked in previous works. We hope that the discussion and results presented in this article reinvigorates interest in density matrix minimization methods.