On the Chemical Potential of Many-Body Perturbation Theory in Extended Systems

Area of Science:

• Computational Physics
• Quantum Chemistry
• Condensed Matter Theory

Background:

• Finite-temperature many-body perturbation theory is crucial for electronic properties at nonzero temperatures.
• Current methods often require iterative searches for the chemical potential, increasing computational expense.
• Extended systems with mobile charges present unique challenges due to electrostatic forces.

Purpose of the Study:

• To demonstrate that per-electron properties in extended systems are independent of chemical potential.
• To eliminate the need for iterative chemical potential searches in finite-temperature calculations.
• To introduce a computationally efficient approach for calculating electronic properties.

Main Methods:

• Utilized finite-temperature many-body perturbation theory in the grand-canonical ensemble.
• Applied Spencer-Alavi regularization for Coulomb interaction in extended systems.
• Employed finite-temperature Hartree approximation and linearized finite-temperature direct-ring coupled-cluster doubles for calculations.

Main Results:

• Showed that exchange-correlation free energy and grand potential per electron agree in the infinite-size limit.
• Confirmed that properties per electron are independent of chemical potential in extended systems.
• Demonstrated the effectiveness of Coulomb interaction regularization, avoiding interactions with periodic images.

Conclusions:

• A single, non-iterative correlation calculation suffices for each system size, significantly reducing computational cost.
• The findings simplify and accelerate electronic property calculations for extended systems at finite temperatures.
• This method offers a more efficient pathway for accurate quantum mechanical simulations.