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

Area of Science:

• Computational physics
• Quantum chemistry
• Materials science

Background:

• Accurate calculation of electronic structure at finite temperatures is crucial for understanding material properties.
• Existing methods for density matrix calculation can face challenges with physicality and computational scaling.
• The Fermi-Dirac density matrix is fundamental for describing systems in thermal equilibrium.

Purpose of the Study:

• To introduce a novel, physically constrained method for computing the Fermi-Dirac density matrix.
• To demonstrate the efficiency and scalability of the proposed method for electronic structure problems.
• To provide a robust alternative for finite-temperature electronic structure calculations.

Main Methods:

• Wave Operator Minimization (WOM) method is presented, utilizing the wave operator (square root of the density matrix).
• The method models a cooling process from an infinite temperature state to a target finite temperature.
• Both grand canonical and canonical ensembles are considered for the calculations.

Main Results:

• The WOM method ensures physicality by construction through the use of the wave operator.
• The convergence rate of the WOM method is independent of the number of atoms in the system, indicating excellent scalability.
• Successful application to electronic structure problems at finite temperatures is demonstrated.

Conclusions:

• Wave Operator Minimization offers a physically sound and computationally efficient approach for finite-temperature electronic structure calculations.
• The method's scalability suggests its applicability to large and complex systems.
• This work aims to stimulate further research into density matrix minimization techniques.