Refining and relating fundamentals of functional theory

Area of Science:

• Quantum Chemistry
• Condensed Matter Physics
• Computational Many-Body Theory

Background:

• One-particle reduced density matrix functional theory (1RDMFT) is a powerful tool for electronic structure calculations.
• Understanding the fundamental concepts of 1RDMFT, such as scope, natural variables, and v-representability, is crucial for its advancement.
• Exploiting symmetries, particularly time-reversal symmetry, can lead to deeper insights into the theory.

Purpose of the Study:

• To refine and relate fundamental features and concepts of 1RDMFT.
• To define the scope and identify natural variables for 1RDMFT.
• To investigate the role of symmetries, specifically time-reversal symmetry, and their impact on universal functionals and v-representability.

Main Methods:

• Analytical derivation of pure and ensemble functionals for the Hubbard dimer and its generalizations.
• Exploitation of time-reversal symmetry to identify and relate six equivalent universal functionals.
• Investigation of v-representability for various functionals with respect to real- and complex-valued Hilbert spaces.

Main Results:

• Established concise definitions for the scope and natural variables of 1RDMFT.
• Demonstrated the existence of six equivalent universal functionals for systems with time-reversal symmetry and proved relations among them.
• Solved v-representability problems analytically for the Hubbard dimer, showing dependence on pair interactions and revealing repulsive divergence of functional gradients at domain boundaries.

Conclusions:

• The notion of v-representability is relative to the chosen scope and variables in 1RDMFT.
• The repulsive divergence of universal functional gradients emphasizes the universal character of the fermionic exchange force.
• This work provides a more rigorous foundation for 1RDMFT and offers insights into electron correlation effects.