Density functional approach to quantum lattice systems

Abstract

For quantum lattice systems, we consider the problem of characterizing the set of single-particle densities,ρ, which come from the ground-state eigenspace of someN-particle Hamiltonian of the form$H_0 + \sum\nolimits_{i = 1}^N {v(x_i )}$ whereH ₀ is a fixed, bounded operator representing the kinetic and interaction energies. We show that the conditions onρ are that it be strictly positive, properly normalized, and consistent with the Pauli principle. Our results are valid for both finite and infinite lattices and for either bosons or fermions. The Coulomb interaction may be included inH ₀ if the lattice dimension is ⩾2. We also characterize those single-particle densities which come from the Gibbs states of such Hamiltonians at finite temperature. In addition to the conditions stated above,ρ must satisfy a finite entropy condition.