Applications of Coupled Cluster Theory to Models of Extended Systems of Fermions

This thesis describes the application of coupled-cluster theory to model systems of metallic solids and cold-atom gases. First, I give an overview of both ground- and excited-state coupled cluster theory as background for the main topics in this thesis. Next, I evaluate the accuracy of several cost-saving approaches in estimating the coupled cluster correlation energy for a model metallic system, the uniform electron gas, in the complete basis set and thermodynamic limits. After that, I present calculations of the spectral function of the uniform electron gas in these same limits, the results of which are rationalized by applying a bosonized coupled-cluster theory to an approximate, simplified Hamiltonian that couples plasmons to a structureless core hole state. Finally, I show how coupled-cluster theory captures the many-body nature of two-component Fermi gases with tunable, attractive interactions.