Recorded 01 April 2025. Julia Liebert of Ludwig-Maximilians-Universität München presents "Ensemble density matrix functional theory for excited states" at IPAM's Optimal Transport for Density Operators: Theory and Numerics Workshop. Abstract: Reduced density matrix theories offer a promising tool to circumvent the exponential scaling of the N-fermion Hilbert space with the system size. Furthermore, addressing quantum systems with strong correlations is a central challenge in modern quantum chemistry and condensed matter physics. Therefore, this talk focuses on one-particle reduced density matrix functional theory (RDMFT), which is well-suited for describing strongly correlated many-particle systems. We first introduce a w-ensemble RDMFT that variationally targets ensembles of low-lying excited states with a fixed spectrum. Afterwards, we employ tools from convex analysis to solve the N-representability problem. Remarkably, this reveals that essential information about the excitation structure of molecular systems is embedded in the functional's domain. Additionally, we derive a generalization of Pauli’s exclusion principle for mixed states and and explore their extension in the context of spin symmetries. To advance the development of more accurate functionals, we provide in the second part of the talk the theoretical foundations for ensemble Hartree-Fock theory for excited states by extending Lieb’s variational principle to w-ensembles. For this, we work out three essential properties that any underlying Hartree-Fock functional must satisfy and systematically derive a functional that satisfies all of them by leveraging the one-to-one correspondence between free states and one-particle reduced density matrices. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-i-optimal-transport-for-density-operators-theory-and-numerics/?tab=schedule