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

• URL: http://arxiv.org/abs/2204.12715v2
• Date: Tue, 27 Sep 2022 15:24:06 GMT
• Title: An exact one-particle theory of bosonic excitations: From a generalized Hohenberg-Kohn theorem to convexified N-representability
• Authors: Julia Liebert, Christian Schilling
• Abstract summary: We propose a functional theory for targeting low-lying excitation energies of bosonic quantum systems through the one-particle picture. We employ an extension of the Rayleigh-Ritz variational principle to ensemble states with spectrum $boldsymbolw$ and prove a corresponding generalization of the Hohenberg-Kohn theorem. Remarkably, this reveals a complete hierarchy of bosonic exclusion principle constraints in conceptual analogy to Pauli's exclusion principle for fermions.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\boldsymbol{w}$ 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 $\boldsymbol{w}$-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 $\boldsymbol{w}$-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.

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