Tomasz Maciazek

Deriving ansatz wave functions for ground states of multi electron systems from extremal single particle information

My presented results can be viewed as a generalisation of the Hartree-Fock method where ground states of multi electron systems are assumed to have the form of a single Slater determinant. My main object of interest is the so-called spectral polytope (aka the momentum polytope in symplectic geometry) which is a convex polytope formed by the (ordered) spectra of one-particle reduced density matrices coming from the reduction of a pure state. Inequalities describing faces of such a polytope generalise the well-known Pauli exclusion principle which states that occupation numbers of a multi electron quantum state are between 0 and 1. I will explain that saturation of such generalised Pauli inequalities has strong implications for the structure of the multi electron quantum state leading to different families of variational ansatz wave functions. Throughout, I will introduce relevant notions from symplectic geometry that are necessary to derive the above selection rules.