Accelerating Auxiliary-Field Quantum Monte Carlo Simulations of Solids with Graphical Processing Units

Area of Science:

• Computational Physics
• Materials Science
• Quantum Chemistry

Background:

• Auxiliary-field quantum Monte Carlo (AFQMC) is a powerful method for simulating quantum systems.
• Simulations of solid state systems are computationally demanding.
• Accelerating these simulations is crucial for advancing materials discovery.

Purpose of the Study:

• To accelerate AFQMC simulations of solid state systems using GPUs.
• To optimize AFQMC algorithms for efficient GPU utilization.
• To demonstrate the capability of GPU-accelerated AFQMC for accurate materials property prediction.

Main Methods:

• Leveraging crystal momentum conservation in one- and two-electron integrals.
• Developing efficient algorithms tailored for GPU architectures.
• Implementing and profiling AFQMC on GPUs, comparing performance against CPU implementations.

Main Results:

• Achieved a 40-fold speedup in AFQMC simulations compared to CPU implementations.
• Demonstrated efficient utilization of GPU architectures through algorithmic optimization.
• Successfully computed the cohesive energy of carbon in the diamond structure with high accuracy (0.02 eV from experiment).

Conclusions:

• GPU acceleration significantly enhances the computational efficiency of AFQMC for solid state systems.
• The optimized AFQMC approach enables systematic convergence of calculations with respect to basis set and system size.
• This work paves the way for more complex and accurate simulations in condensed matter physics and materials science.