Foundation of oneparticle reduced density matrix functional theory for excited states
Abstract
In [Phys. Rev. Lett. 127, 023001 (2021)] a reduced density matrix functional theory (RDMFT) has been proposed for calculating energies of selected eigenstates of interacting manyfermion systems. Here, we develop a solid foundation for this socalled $\boldsymbol{w}$RDMFT and present the details of various derivations. First, we explain how a generalization of the Ritz variational principle to ensemble states with fixed weights $\boldsymbol{w}$ in combination with the constrained search would lead to a universal functional of the oneparticle reduced density matrix. To turn this into a viable functional theory, however, we also need to implement an exact convex relaxation. This general procedure includes Valone's pioneering work on ground state RDMFT as the special case $\boldsymbol{w}=(1,0,\ldots)$. Then, we work out in a comprehensive manner a methodology for deriving a compact description of the functional's domain. This leads to a hierarchy of generalized exclusion principle constraints which we illustrate in great detail. By anticipating their future pivotal role in functional theories and to keep our work selfcontained, several required concepts from convex analysis are introduced and discussed.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 DOI:
 10.48550/arXiv.2106.03918
 arXiv:
 arXiv:2106.03918
 Bibcode:
 2021arXiv210603918L
 Keywords:

 Quantum Physics;
 Condensed Matter  Strongly Correlated Electrons;
 Mathematical Physics
 EPrint:
 published version