Ab Initio Computations Of Structural Properties In Solids By Auxiliary Field Quantum Monte Carlo

Determining the accurate structure of a material is a critical step in understanding its physics. Standard electronic structure methods have not achieved systematic accuracy, especially for materials with strong electron correlation effects. Many-body methods can potentially deliver higher accuracy, but they all face significant algorithmic obstacles for structural optimization in solids. In this thesis, I present a direct, ab initio computation of forces and stresses with auxiliary field quantum Monte Carlo (AFQMC). AFQMC is a many-body computational method that has shown excellent performance in computing the total energy and charge density. Our method for computing forces and stresses requires minimal approximations and can be used to predict the potential energy surface at a much higher efficiency than an energy-only approach. In addition, we propose a fast and robust structural optimization algorithm with statistically noisy forces. Applying this algorithm to our forces and stresses, we demonstrate efficient, accurate, and full degrees-of-freedom optimizations in solids. Phonon calculations also become more efficient with AFQMC forces, though a naive frozen-phonon approach amplifies noises and struggles to retrieve the signal. We solve this problem by proposing a population control scheme in the correlated sampling framework, obtaining fast and accurate phonon spectra for solids. Finally, we demonstrate the possibility of computing Berry phases, polarizations, and the Chern number in AFQMC with a correlated sampling based algorithm. The systematic methods and techniques in this thesis pave the way for a wide range of applications, including but not limited to prediction of structures, thermodynamics, ferroelectricity, and topological properties of quantum materials