Positivity preserving density matrix minimization at finite temperatures via square root.

The article presents the Wave Operator Minimization (WOM) method for calculating the Fermi–Dirac density matrix at finite temperatures in electronic structure problems, applicable to both grand canonical (constant chemical potential) and canonical (constant electron number) ensembles. WOM operates by minimizing the square root of the density matrix—referred to as the wave operator—modeling the cooling of a system from infinite to finite temperature, and explicitly preserves physical constraints such as positivity and Hermiticity. The method demonstrates convergence steps independent of system size and is validated through tight-binding models of aluminum and silicon, showing comparable efficiency to the Fermi operator expansion (FOE) method while addressing some of FOE’s limitations. The authors provide an adaptive numerical implementation and make the code publicly available, suggesting WOM as a promising computational tool for scalable finite-temperature electronic structure calculations.