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

TL;DR

This paper develops an ensemble reduced density matrix functional theory (RDMFT) for excited states, overcoming historical obstacles by using convex analysis and a generalized exclusion principle, enabling accurate energy calculations for many-electron systems.

Contribution

It introduces a novel RDMFT framework for excited states, employing convex analysis and a hierarchical exclusion principle, extending the applicability of RDMFT beyond ground states.

Findings

Established a universal functional for excited states.

Derived linear constraints for systems of arbitrary size.

Revealed a hierarchical generalization of Pauli's exclusion principle.

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.