Hamiltonian formulation of weighted-ensemble density-functional theory

Abstract

A Hamiltonian formulation of weighted-ensemble density-functional theory is provided by considering eigenstates of a super-Hamiltonian that consists of a sum of replicas of the physical Hamiltonian. For a nondegenerate physical Hamiltonian the replica permutational symmetry specified by the Young diagram $\ensuremath{\Gamma}\ensuremath{\equiv}[{\ensuremath{\lambda}}_{1},{\ensuremath{\lambda}}_{2},\dots{}],$ where ${\ensuremath{\lambda}}_{1}>~{\ensuremath{\lambda}}_{2}>~\ensuremath{\cdot}\ensuremath{\cdot}\ensuremath{\cdot}$ and $|\ensuremath{\Gamma}|={\ensuremath{\sum}}_{i}{\ensuremath{\lambda}}_{i},$ yields a super-ground state, which is equivalent to an ensemble average with weights ${\ensuremath{\omega}}_{i}={\ensuremath{\lambda}}_{i}/|\ensuremath{\Gamma}|,$ $i=1,2,\dots{}.$ A corresponding Hohenberg-Kohn theorem is derived, and an extension to degenerate physical Hamiltonians is proposed.