Deriving density-matrix functionals for excited states

Abstract

We initiate the recently proposed $\mathbf{w}$-ensemble one-particle reduced density matrix functional theory ($\mathbf{w}$-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 $\mathbf{w}$-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.

Application of w-RDMFT which has been proposed in arXiv:2204.12715; close to published version

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Cited by in corpus (12)

• Exact Excited-State Functionals of the Asymmetric Hubbard Dimer
• An exact one-particle theory of bosonic excitations: From a generalized Hohenberg-Kohn theorem to convexified N-representability
• Ground and Excited States from Ensemble Variational Principles
• Neutral electronic excitations and derivative discontinuities: An extended $N$-centered ensemble density functional theory perspective
• Ensemble density functional theory of ground and excited energy levels
• Extended $N$-centered ensemble density functional theory of double electronic excitations
• Extracting Many-Body Quantum Resources within One-Body Reduced Density Matrix Functional Theory
• Exact static linear response of excited states from ensemble density functional theory
• Capturing electron correlation at mean-field cost: Assessment of i-DMFT and the underlying correlation conjecture
• Solving one-body ensemble N-representability problems with spin
• Spin adaptation of the cumulant expansions of reduced density matrices
• Refining ensemble $N$-representability of one-body density matrices from partial information