Ab Initio Finite Temperature Auxiliary Field Quantum Monte Carlo

Area of Science:

• Computational Chemistry
• Quantum Many-Body Physics
• Materials Science

Background:

• Accurate electronic structure calculations are crucial for understanding molecular and material properties.
• Finite-temperature simulations present significant challenges due to the phase problem in quantum Monte Carlo methods.

Purpose of the Study:

• To introduce a novel ab initio auxiliary field quantum Monte Carlo method for finite-temperature electronic structure studies.
• To combine high-accuracy ground-state methods with finite-temperature techniques for improved simulations.
• To address and mitigate the phase problem in quantum Monte Carlo calculations.

Main Methods:

• Developed an ab initio phaseless auxiliary field quantum Monte Carlo algorithm for finite temperatures.
• Integrated ground-state and finite-temperature variants of the auxiliary field quantum Monte Carlo method.
• Employed importance sampling to control the phase problem, often obviating the need for the phaseless approximation.

Main Results:

• Achieved internal energies within chemical accuracy compared to exact diagonalization for H2O, C2, 1D hydrogen chains, and the Hubbard model.
• Demonstrated the method's effectiveness across a wide temperature range, approaching ground-state accuracy.
• Showcased the versatility for studying finite-temperature phase diagrams of complex systems.

Conclusions:

• The presented method offers a robust and accurate approach for finite-temperature electronic structure calculations.
• The phase problem's severity is notably higher for model Hamiltonians than for many molecules.
• This technique provides a versatile tool for exploring diverse quantum systems beyond simple models.