Ensemble Density Matrix Functional Theory for Excited States

Explore a 39-minute lecture by Julia Liebert from Ludwig-Maximilians-Universität München on "Ensemble density matrix functional theory for excited states," recorded at IPAM's Optimal Transport for Density Operators workshop at UCLA on April 1, 2025. Discover how reduced density matrix theories can overcome the exponential scaling challenges of N-fermion Hilbert spaces while effectively addressing strongly correlated quantum systems. Learn about w-ensemble RDMFT for targeting low-lying excited states with fixed spectra, and how convex analysis tools solve the N-representability problem—revealing that molecular systems' excitation structures are embedded in the functional's domain. The presentation also covers a generalization of Pauli's exclusion principle for mixed states and explores spin symmetry extensions. In the second part, examine the theoretical foundations for ensemble Hartree-Fock theory through the extension of Lieb's variational principle to w-ensembles, including the three essential properties any Hartree-Fock functional must satisfy.