An efficient and accurate decomposition of the Fermi operator

Area of Science:

• Computational physics
• Quantum chemistry
• Materials science

Background:

• Calculating the Fermi function is crucial for understanding fermionic systems.
• Existing methods often face challenges with computational cost and ill-conditioned Hamiltonians.

Purpose of the Study:

• To present a novel, efficient method for computing the Fermi function of independent fermions.
• To develop a scheme that is robust against ill-conditioned Hamiltonians and orbital localization.

Main Methods:

• Exact decomposition of the grand-canonical potential.
• Exploitation of density matrix sparsity for linear scaling.
• Hybrid approach combining polynomial expansion and Newton-like iterative techniques.

Main Results:

• The method demonstrates insensitivity to ill-conditioned Hamiltonians.
• Achieves favorable computational cost scaling with inverse temperature.
• Successfully applied to the density functional theory Hamiltonian of LiAl alloy.

Conclusions:

• The proposed method provides an accurate and computationally efficient way to compute the Fermi function.
• It overcomes limitations of previous techniques, offering competitive performance.
• The approach is well-suited for large-scale electronic structure calculations.