Semistochastic projector Monte Carlo method.

Area of Science:

• Computational physics
• Quantum chemistry
• Numerical analysis

Background:

• Calculating dominant eigenvalues and eigenvector expectation values for large matrices is computationally intensive.
• Stochastic methods, like quantum Monte Carlo, are often used but can be slow to converge.
• Systems with a sign problem pose additional challenges for traditional computational methods.

Purpose of the Study:

• To introduce a novel semistochastic implementation of the power method.
• To significantly reduce computational time for determining dominant eigenvalues and eigenvector expectation values.
• To demonstrate the method's efficacy on challenging systems, including those with a sign problem.

Main Methods:

• A semistochastic approach combining exact numerical matrix multiplication with stochastic computation for expectation values.
• Application of the semistochastic quantum Monte Carlo method.
• Testing on the fermion Hubbard model and the carbon dimer.

Main Results:

• The semistochastic power method substantially decreases the computational time needed to achieve a desired statistical uncertainty in eigenvalue calculations.
• The method successfully computed dominant eigenvalues and expectation values for systems exhibiting a sign problem.
• Performance was validated on the fermion Hubbard model and carbon dimer.

Conclusions:

• The semistochastic power method offers a significant computational advantage over fully stochastic methods for large matrices.
• This approach provides an efficient means to tackle complex quantum systems, particularly those with sign problems.
• The method is a valuable tool for advancing research in computational physics and quantum chemistry.