Scalable Quantum Monte Carlo Method for Polariton Chemistry via Mixed Block Sparsity and Tensor Hypercontraction...

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Auxiliary-field quantum Monte Carlo (AFQMC) is a powerful method for electronic structure calculations.
• Scaling limitations of traditional AFQMC hinder its application to large molecular systems.

Purpose of the Study:

• To develop a reduced-scaling AFQMC framework for large molecular systems and ensembles.
• To improve the efficiency of exchange-energy evaluation in AFQMC.

Main Methods:

• Leveraging block sparsity in Cholesky decomposition (CD) of electron repulsion integrals.
• Employing tensor hypercontraction (THC) to compress low-rank Cholesky blocks.
• Utilizing a mixed format for Cholesky vectors (block-sparse and THC-compressed).

Main Results:

• Reduced scaling of exchange-energy evaluation from quartic to cubic with respect to the number of molecular orbitals (N).
• Lowered memory requirements from cubic to near-quadratic.
• Demonstrated linear growth of nonzeros in Cholesky tensors and sublinear increase in average numerical rank with system size.
• Achieved cubic wall-time scaling with favorable prefactors and preserved AFQMC accuracy.

Conclusions:

• The proposed mixed block sparsity and THC scheme efficiently calculates exchange energy for large molecular ensembles.
• This framework significantly enhances the applicability of AFQMC to large-scale quantum chemistry problems.