UC Berkeley

The theoretical description of many-body systems, be it molecular or extended, from first principles has been one of the principal goals of the physical sciences since the advent of quantum mechanics. This is unfortunately an exceptionally complicated endeavour, especially so in the so called ``strongly correlated'' systems. These are characterized by their qualitative behavior being dominated by particle-particle interactions, which precludes their accurate description using effective one-body approaches, such as Kohn-Sham density-functional theory. As a consequence of their remarkable complexity, strongly correlated materials present a wide palette of exciting collective phenomena of huge technological interest. Paradigmatic examples are high temperature superconductors based on transition metal oxides or pnictides, materials presenting colossal magnetoresistance, or iron/molybdenum based catalytic centers in biological systems. With the ample range of potential applications in mind, from energy conversion and storage to the development of new principles for information processing devices, great interdisciplinary effort, combining condensed matter physics, quantum chemistry and materials science, has been dedicated over the last decades to devising and applying accurate theoretical and numerical approaches for the description and prediction of electronic properties arising from strong correlation.

Unfortunately, due to the rich variety of physical and chemical principles which can result in strongly correlated behavior, there is currently no single method which can be successfully applied to all correlated many-body systems. On the contrary, a broad toolkit composed of analytical theories and computational approaches has been developed over the years, each based on a different heuristic to simplify the solution of the problem, and therefore each being applicable accurately on a different class of many-body system. In this thesis, we have refined and developed one such tool in the many-body toolbox: the adaptive sampling configuration interaction (ASCI) method. This is an exceptionally efficient selective configuration interaction approach, originally formulated to provide accurate ground state energies of molecular systems with a moderate computational cost. Here, we further extend the ASCI framework to compute accurate spectral properties, accessible through the one-body Green's function, allowing us to study excited state properties as well as to apply ASCI to extended systems by using it as impurity solver within the dynamical mean-field theory (DMFT). This makes ASCI noticeably versatile, and we employ it to contribute to open problems in quantum computation, molecular physics and computational condensed matter theory. This wide applicability shows ASCI to be a useful new addition to the many-body theory tool-set. In particular the ASCI-DMFT approach introduced here holds great promise for the \emph{ab initio} study of strongly correlated materials.