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Deriving density-matrix functionals for excited states
by Julia Liebert, Christian Schilling
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Christian Schilling |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202303_00003v1 (pdf) |
| Date accepted: | 2023-03-28 |
| Date submitted: | 2023-03-02 17:55 |
| Submitted by: | Schilling, Christian |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We initiate the recently proposed $\boldsymbol{w}$-ensemble one-particle reduced density matrix functional theory ($\boldsymbol{w}$-RDMFT) by deriving the first functional approximations and illustrate how excitation energies can be calculated in practice. For this endeavour, we first study the symmetric Hubbard dimer, constituting the building block of the Hubbard model, for which we execute the Levy-Lieb constrained search. Second, due to the particular suitability of $\boldsymbol{w}$-RDMFT for describing Bose-Einstein condensates, we demonstrate three conceptually different approaches for deriving the universal functional in a homogeneous Bose gas for arbitrary pair interaction in the Bogoliubov regime. Remarkably, in both systems the gradient of the functional is found to diverge repulsively at the boundary of the functional's domain, extending the recently discovered Bose-Einstein condensation force to excited states. Our findings highlight the physical relevance of the generalized exclusion principle for fermionic and bosonic mixed states and the curse of universality in functional theories.
List of changes
1) We corrected the typos in Eqs. (14) and (15) (Eqs. (13) and (14) in the new manuscript) and the line above Eq. (14).
2) We modified the paragraph below Eq. (4) .
3) We added the lower convex envelope operation to the rhs in Eq. (40) and modified the paragraph around Eq. (40).
4) We modified the paragraph below Eq. (43).
5) We modified the last paragraph of Sec. IV.E.2.
6) We modified the first paragraph of Sec. IV.E.3.
7) We updated the end of the second paragraph of Sec. V.
Published as SciPost Phys. 14, 120 (2023)
Reports on this Submission
Report #1 by Klaas Giesbertz (Referee 1) on 2023-3-2 (Invited Report)
Report
The authors have addressed all raised points adequately.