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تسجيل مستخدم جديدFoundation of one-particle reduced density matrix functional theory for excited states
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In [arxiv:2106.02560] we proposed a reduced density matrix functional theory (RDMFT) for calculating energies of selected eigenstates of interacting many-fermion systems. Here, we develop a solid foundation for this so-called $boldsymbol{w}$-RDMFT and present the details of various derivations. First, we explain how a generalization of the Ritz variational principle to ensemble states with fixed weights $boldsymbol{w}$ in combination with the constrained search would lead to a universal functional of the one-particle reduced density matrix. To turn this into a viable functional theory, however, we also need to implement an exact convex relaxation. This general procedure includes Valones pioneering work on ground state RDMFT as the special case $boldsymbol{w}=(1,0,ldots)$. Then, we work out in a comprehensive manner a methodology for deriving a compact description of the functionals domain. This leads to a hierarchy of generalized exclusion principle constraints which we illustrate in great detail. By anticipating their future pivotal role in functional theories and to keep our work self-contained, several required concepts from convex analysis are introduced and discussed.
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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 u
nfeasible 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 Valones pioneering work on RDMFT as a special case of convex relaxation and reveals that crucial information about the excitation structure is contained in the functionals 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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