Communication: Generalized canonical purification for density matrix minimization.

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• The N-representable one-particle density matrix is crucial for electronic structure calculations.
• Existing methods for finding the density matrix can be computationally intensive.

Purpose of the Study:

• To propose a novel Lagrangian formulation for the constrained search of the N-representable one-particle density matrix.
• To develop a method that systematically converges to the ground state.
• To offer a computationally efficient alternative to traditional diagonalization techniques.

Main Methods:

• Utilizing a Lagrangian formulation based on McWeeny idempotency error minimization.
• Deriving a closed form for canonical purification.
• Exploring generalizations through hole-particle duality.

Main Results:

• The proposed method systematically converges to the ground state.
• A closed-form canonical purification eliminates the need for a posteriori trace adjustment.
• The method demonstrates potential for solving dense and sparse matrix eigenvalue problems.

Conclusions:

• The developed Lagrangian formulation provides an efficient and systematic route to the N-representable one-particle density matrix.
• Its simplicity and low computational complexity make it a viable alternative to diagonalization.
• The method offers potential for broader applications in quantum mechanical calculations.