Local Spectral Formulation of the One-Determines-All (ODA) Principle for Multistate Density Functionals

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Multistate density functional theory (MSDFT) extends Kohn-Sham DFT to model systems with multiple interacting electronic states.
• A key challenge is developing matrix functionals that maintain unitary invariance and capture state coupling.

Purpose of the Study:

• To establish a rigorous framework for constructing local, unitary-covariant matrix functionals in MSDFT.
• To simplify the calculation of matrix functionals by relating them to scalar functions.

Main Methods:

• Developed a theoretical approach showing local, unitary-covariant matrix functionals are codiagonalizable with the matrix density.
• Demonstrated a one-to-all mapping from a scalar generator to the matrix functional based on eigenvalues.
• Applied the formalism to a four-state Hubbard model for validation.

Main Results:

• Any local, unitary-covariant matrix functional is fully defined by a scalar generator acting on the eigenvalues of the matrix density.
• The construction of N^2 matrix elements reduces to a single scalar mapping evaluated on the eigenvalue spectrum.
• Exact reconstruction was achieved for a four-state Hubbard model, demonstrating the formalism's validity.

Conclusions:

• The study provides a rigorous foundation for creating local matrix exchange-correlation functionals in MSDFT.
• This approach significantly reduces computational complexity, making MSDFT approximations more scalable and comparable to standard DFT.
• Offers a practical pathway for developing efficient and accurate MSDFT methods for complex quantum systems.