N-representable parametrization of the 2RDMs based on a new compact formalism

Friday 08 July 2022, 14:00

Thierry Deutsch

In this talk, I intend to show a new formalism that solves the famous many-body problem of quantum mechanics with a complexity varying as a function of n⁴ where n is the number of states. The reduced two-body density matrix (2-RDM) had this complexity but to be N-representable, a gigantic number of conditions must be taken into account.

Based on anti-commutativity relations, we show that we can construct a pair of anti-commutation matrices, (ACDM) that are isomorphic to many-body wavefunctions but have the advantage of being compactable. Thanks to this new formalism, we show that the 2-RDM of the wavefunctions solutions of a two-body interaction Hamiltonian can be represented exactly thanks to ACDM submitted to some equality constraints. We show that these ACDM constraints are necessary and sufficient.
We will give also a new geometric interpretation of the 2-RDM and we will develop the Lagrangian and illustrate with numerical examples.

The video is available here.