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Abstract
Strong electron correlation is a significant feature in the electronic structure of a variety of molecules and materials with applications to technologically relevant processes like charge and energy transfer. Strong correlation is particularly important in materials that exhibit phenomena driven by quantum entanglement, such as superconductivity and exciton condensation. However, modeling strong correlation accurately and efficiently is a challenge for many electronic structure methods. In this work, strongly correlated phenomena, with specific focus on superconductivity and exciton condensation, are explored from the perspective of reduced density matrices. Reduced density matrix (RDM) methods are inherently well-suited to modeling the multiconfigurational nature of strong correlation and can do so at reasonable computational cost. Moreover, there are signatures for quantum entanglement and off-diagonal long-range order associated with superconductivity and exciton condensation found in RDMs. Using this framework, methods for characterizing exciton condensation based on a signature in the particle-hole RDM are presented. The particlehole RDM signature, and a related signature for superconductivity from the two-electron RDM, are also applied to identifying the microscopic beginnings of exciton condensation and superconductivity in several molecular-scale systems. An electronic structure method based on the two-electron RDM is generalized to periodic systems for elucidation of strong correlation at the materials scale. This method is applied to several strongly correlated materials in conjunction with the presentation of a natural orbital occupation-based method for characterizing electronic band structure. Finally, connections between exciton condensation and exciton correlation and entanglement in photosynthetic light-harvesting are examined, demonstrating that even without macroscopic condensation, localized exciton-condensate-like states can play a significant role in energy transfer.