Positivity Preserving Density Matrix Minimization at Finite Temperatures via Square Root

TL;DR

This paper introduces a Wave Operator Minimization method that computes the Fermi-Dirac density matrix at finite temperatures, ensuring physical positivity and efficiency regardless of system size.

Contribution

The proposed WOM method uniquely models temperature cooling and guarantees positivity, with convergence independent of system size, advancing density matrix minimization techniques.

Findings

Converges efficiently regardless of atom count

Ensures positivity of the density matrix by construction

Applicable to both grand canonical and canonical ensembles

Abstract

We present a Wave Operator Minimization (WOM) method for calculating the Fermi-Dirac density matrix for electronic structure problems at finite temperature while preserving physicality by construction using the wave operator, i.e., the square root of the density matrix. WOM models cooling a state initially at infinite temperature down to the desired finite temperature. We consider both the grand canonical (constant chemical potential) and canonical (constant number of electrons) ensembles. Additionally, we show that the number of steps required for convergence is independent of the number of atoms in the system. We hope that the discussion and results presented in this article reinvigorates interest in density matrix minimization methods.