UBC Math Department Colloquium: Augusto Gerolin

Reduced density matrix theories offer a promising tool to circumvent the exponential scaling of the N-fermion Hilbert space with the system size and it is conceptually well-suited to describe strongly correlated many-particle systems, a central challenge in modern quantum chemistry and condensed matter physics.

In this talk, we demonstrate how the exact reduced density matrix functional can be expressed as a (regularized) quantum optimal transport problem. This provides a mathematical framework and computational platform for exploration of the exact functional and its derivative. Our approach is practical even for strongly-correlated electrons (where density-matrix functional theory may be expected to surpass density functional theory) and can be applied to molecules larger than those considered by analogous density-functional problems.