An accelerated linear method for optimizing non-linear wavefunctions in variational Monte Carlo.

Area of Science:

• Computational Quantum Chemistry
• Electronic Structure Theory

Background:

• Variational Monte Carlo (VMC) methods are crucial for quantum mechanical calculations.
• Optimizing nonlinearly parametrized wavefunctions in VMC typically uses robust linear methods.
• Existing linear methods face memory bottlenecks due to storing large Hamiltonian and overlap matrices.

Purpose of the Study:

• To develop a more memory-efficient and scalable optimization algorithm for VMC.
• To reduce the computational cost associated with optimizing complex wavefunctions.
• To apply the improved optimization technique to a variety of quantum systems.

Main Methods:

• Implementation of the Jacobi-Davidson algorithm to iteratively solve the generalized eigenvalue problem.
• Avoidance of explicit matrix construction and storage, reducing memory requirements.
• Hybrid optimization strategy combining AMSGrad for initial phases and the direct linear method for final convergence.

Main Results:

• The direct linear method significantly lowers computational cost and improves scaling with the number of parameters.
• The hybrid approach enhances optimization efficiency for wavefunctions with many parameters.
• Successful application to diverse systems including atoms, molecules, and model Hamiltonians.

Conclusions:

• The Jacobi-Davidson based direct linear method offers a substantial improvement over traditional linear methods in VMC.
• The developed hybrid optimization strategy provides a computationally efficient pathway for complex quantum system studies.
• This work paves the way for more accurate and feasible electronic structure calculations.