Some recent developments in auxiliary-field quantum Monte Carlo for real materials.

Area of Science:

• Computational Physics
• Quantum Chemistry
• Materials Science

Background:

• The auxiliary-field quantum Monte Carlo (AFQMC) method is a versatile numerical technique for simulating correlated many-electron systems.
• AFQMC finds increasing application across diverse areas including lattice models, atoms, molecules, and solids.

Purpose of the Study:

• To introduce the theory and algorithms of AFQMC specifically tailored for real materials.
• To present recent advancements and provide a systematic exposition of key AFQMC steps within a modern software library framework.

Main Methods:

• Detailed discussion of core AFQMC steps: Monte Carlo Hamiltonian construction, ground state projection, two-body operator sampling, and the phaseless approximation.
• Implementation of multi-determinant trial wave functions to accelerate computations and reduce memory requirements.
• Proposal and discussion of a self-consistent constraint for real materials, utilizing coupling to independent-electron calculations or natural orbitals.

Main Results:

• The presented methods enable efficient and accurate simulations of correlated many-electron systems in real materials.
• Advanced implementation significantly improves computational speed and reduces memory footprint.
• The self-consistent constraint offers flexible and effective approaches for material property calculations.

Conclusions:

• The specialized AFQMC method provides a robust framework for investigating electronic properties of real materials.
• Recent developments, including advanced implementations and self-consistent constraints, enhance the practicality and applicability of AFQMC.
• This work lays the foundation for a modern software library, facilitating broader adoption of AFQMC in materials science research.