Submatrix and GPU-accelerated implementation of density matrix tight-binding.

Area of Science:

• Computational Materials Science
• Quantum Chemistry
• Solid-State Physics

Background:

• Single-particle theories like Hartree-Fock and DFT face computational limits due to the self-consistent field (SCF) procedure's cubic scaling.
• Large-scale applications are impractical without advanced algorithms and hardware.
• The PTB tight-binding potential is a key method in this field.

Purpose of the Study:

• To implement and evaluate GPU-accelerated and submatrix methods for the PTB tight-binding potential.
• To overcome the computational bottlenecks of traditional SCF procedures.
• To enable simulations of larger and more complex material systems.

Main Methods:

• Benchmarking traditional diagonalization-based SCF solvers against density-matrix purification approaches.
• Implementing a decomposition-type submatrix method for efficient computation.
• Utilizing graphical processing units (GPUs) for accelerated calculations.
• Systematic variation of system size and computer hardware.

Main Results:

• GPU acceleration achieved a 10-15-fold performance speedup, enabling simulations of larger systems.
• The submatrix method reduced computational cost for systems with approximately 10^4 basis functions.
• Acceptable numerical accuracy was maintained with the submatrix approach.

Conclusions:

• The combination of GPU acceleration and the submatrix method significantly enhances the efficiency of tight-binding calculations.
• This work pushes the boundaries of feasible system sizes in computational materials science.
• The findings highlight the importance of hardware-algorithm interplay for future developments.