Positivity preserving density matrix minimization at finite temperatures via square root

Jacob M Leamer; William Dawson; Denys I Bondar

doi:10.1063/5.0189864

Positivity preserving density matrix minimization at finite temperatures via square root

J Chem Phys. 2024 Feb 21;160(7):074107. doi: 10.1063/5.0189864.

Authors

Jacob M Leamer¹, William Dawson², Denys I Bondar¹

Affiliations

¹ Department of Physics and Engineering Physics, Tulane University, 6823 St. Charles Ave., New Orleans, Louisiana 70118, USA.
² RIKEN Center for Computational Science, Kobe, Hyogo 650-0047, Japan.

PMID: 38375902
DOI: 10.1063/5.0189864

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 reinvigorate interest in density matrix minimization methods.