Ensemble reduced density matrix functional theory for excited states and hierarchical generalization of Pauli's exclusion principle

• URL: http://arxiv.org/abs/2106.02560v1
• Date: Fri, 4 Jun 2021 15:49:31 GMT
• Title: Ensemble reduced density matrix functional theory for excited states and hierarchical generalization of Pauli's exclusion principle
• Authors: Christian Schilling, Stefano Pittalis
• Abstract summary: We propose and work out a reduced density matrix functional theory (RDMFT) for calculating energies of eigenstates of interacting many-electron systems. Various obstacles which historically have doomed such an approach to be unfeasible are overcome.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose and work out a reduced density matrix functional theory (RDMFT) for calculating energies of eigenstates of interacting many-electron systems beyond the ground state. Various obstacles which historically have doomed such an approach to be unfeasible are overcome. First, we resort to a generalization of the Ritz variational principle to ensemble states with fixed weights. This in combination with the constrained search formalism allows us to establish a universal functional of the one-particle reduced density matrix. Second, we employ tools from convex analysis to circumvent the too involved N-representability constraints. Remarkably, this identifies Valone's pioneering work on RDMFT as a special case of convex relaxation and reveals that crucial information about the excitation structure is contained in the functional's domain. Third, to determine the crucial latter object, a methodology is developed which eventually leads to a generalized exclusion principle. The corresponding linear constraints are calculated for systems of arbitrary size.

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