An exact one-particle theory of bosonic excitations: From a generalized Hohenberg-Kohn theorem to convexified N-representability

Abstract

Motivated by the Penrose-Onsager criterion for Bose-Einstein condensation we propose a functional theory for targeting low-lying excitation energies of bosonic quantum systems through the one-particle picture. For this, we employ an extension of the Rayleigh-Ritz variational principle to ensemble states with spectrum $\mathbf{w}$ and prove a corresponding generalization of the Hohenberg-Kohn theorem: The underlying one-particle reduced density matrix determines all properties of systems of $N$ identical particles in their $\mathbf{w}$-ensemble states. Then, to circumvent the $v$-representability problem common to functional theories, and to deal with energetic degeneracies, we resort to the Levy-Lieb constrained search formalism in combination with an exact convex relaxation. The corresponding bosonic one-body $\mathbf{w}$-ensemble $N$-representability problem is solved comprehensively. Remarkably, this reveals a complete hierarchy of bosonic exclusion principle constraints in conceptual analogy to Pauli's exclusion principle for fermions and recently discovered generalizations thereof.

In particular, bosonic counterpart of fermionic w-RDMFT (arXiv:2106.02560, arXiv:2106.03918) is presented; v2: title has been changed, new section proving a generalization of the Hohenberg-Kohn theorem for w-RDMFT has been added

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Cited by in corpus (13)

• Exact Excited-State Functionals of the Asymmetric Hubbard Dimer
• Deriving density-matrix functionals for excited states
• 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
• 1-matrix functional for long-range interaction energy of two hydrogen atoms
• Extended $N$-centered ensemble density functional theory of double electronic excitations
• Orbital-Free Quasi-Density 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
• Spin adaptation of the cumulant expansions of reduced density matrices
• Refining ensemble $N$-representability of one-body density matrices from partial information
• Solving one-body ensemble N-representability problems with spin