Quantum system partitioning at the single-particle level.

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Computational Physics

Background:

• Quantum systems require partitioning for accurate analysis.
• Existing methods like projector-based embedding have limitations.
• Relativistic quantum chemistry needs efficient decoupling of electronic and positronic states.

Purpose of the Study:

• To present a general framework for quantum system partitioning using subsystem separation by unitary block-diagonalization (SSUB).
• To demonstrate the applicability of SSUB to diverse partitioning strategies, including molecular structure and orbital separations.
• To connect SSUB with existing embedding and relativistic quantum chemistry methods.

Main Methods:

• Application of subsystem separation by unitary block-diagonalization (SSUB) to a Fock operator.
• Formulation of SSUB for a one-particle Hilbert space, allowing general applicability.
• Demonstration of SSUB's relation to projector-based embedding and relativistic exact two-component (X2C) approaches.

Main Results:

• SSUB provides a unified framework embracing various partitioning schemes, including those by Manby, Miller, Huzinaga, and Cantu.
• SSUB simplifies and accelerates projector-based embedding.
• The exact two-component (X2C) approach is shown to be a special case of SSUB, framing it as a system-environment decoupling method.
• SSUB allows for an arbitrary number of subsystems, recovering exact diagonalization in the limit.

Conclusions:

• SSUB offers a versatile and powerful tool for partitioning quantum systems, enhancing both conceptual understanding and computational efficiency.
• The framework facilitates cross-fertilization between different areas of quantum mechanics and computational chemistry.
• SSUB provides a pathway for developing efficient partitioning strategies for large quantum systems, inspired by atomic decomposition in X2C methods.