Foundation of one-particle 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 many-fermion systems. Here, we develop a solid foundation for this so-called $\boldsymbol{w}$-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 one-particle 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 self-contained, several required concepts from convex analysis are introduced and discussed.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2021
- DOI:
- 10.48550/arXiv.2106.03918
- arXiv:
- arXiv:2106.03918
- Bibcode:
- 2021arXiv210603918L
- Keywords:
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- Quantum Physics;
- Condensed Matter - Strongly Correlated Electrons;
- Mathematical Physics
- E-Print:
- published version