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Note: thesis: Thesis (Ph. D.)--Brown University, 2019
Genre (aat): theses
Abstract: The accurate evaluation of quantum mechanical properties of molecules and materials becomes more challenging when highly accurate descriptions of electron correlation are required. Different flavors of theories have been actively developed and successfully applied to a wide array of physical and chemical problems. However, the curse of dimensionality caused by the exponential increase of the Hilbert space limits the scalability and accuracy of most numerical methods. In this thesis, we provide an alternative to conventional wave function techniques by using Auxiliary Field Quantum Monte Carlo (AFQMC) methods which are highly accurate, yet possess a favorable $O(N^3)$ scaling. This thesis mainly describes the accurate modeling of weakly-bound, yet correlated molecules and strongly-correlated materials in which complicated electron correlations are involved by using AFQMC. The first part of this thesis presents the simulation of a fascinating class of weakly-bound species known as dipole-bound anions. The theoretical description of weakly-bound anions remains a challenge, due in part to the relatively weak, yet correlated nature of the dipole interaction ($\sim$ tens to hundreds wave numbers). Here, we demonstrate that a new correlated sampling AFQMC scheme can more successfully predict and obtain the electron binding energies for molecular dipole bound anions than standard, uncorrelated Diffusion Monte Carlo and AFQMC simulations. These results pave the way toward using these approaches for the study of weakly-bound species that are too large to model using traditional electronic structure methods. The second part of this thesis describes the development and application of a theoretical framework for treating the multiband Hubbard Kanamori (HK) model within AFQMC. We elucidate the feasibility and high accuracy of applying AFQMC to the HK model and study the low temperature phase diagram of Ca$_2$RuO$_4$ for a range of layered perovskite structures using AFQMC and DMFT, representing the first application of AFQMC to 4$d$ materials and the first rigorous comparison of AFQMC and DMFT phase diagrams. Our many-body simulations explain the electronic origin of the magnetic and metal-insulator transitions in Ca$_2$RuO$_4$. Portions of the work have been published in Hao \textit{et al}, \textit{J. Phys. Chem. Lett.} 9, 6185, 2018 and Hao \textit{et al}, \textit{Phys. Rev. B} 99, 235142, 2019, which are introduced in Chapters \ref{chapter:2} and \ref{chapter:3}. The work in Chapter \ref{chapter:4} is currently unpublished, but has been prepared for submission to \textit{Phys. Rev. Lett.}.
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Type of Resource (primo): dissertations