Strongly localized quantum crystalline states of the jellium model

Abstract

We consider a system made up of N electrons interacting with a neutralizing positive background within a cubic box of volume V. After dividing the box into N (or N/2) cubic cells for the polarized (unpolarized) case, we average the creation field operator over each cell with a suitable weight function and we consider the quantum crystalline states obtained by letting all the average operators act on the vacuum state. These states exclude the possibility that each cell may momentarily contain more than one or two electrons in the polarized or unpolarized case. The expectation value of the Hamiltonian over this class of states is evaluated in the thermodynamic limit and the weight function is chosen in such a way to minimize the expectation value. The involved numerical analysis is explicitly performed with a weight function having a generalized Gaussian shape depending on a parameter. It turns out that the unpolarized and polarized quantum crystalline states yield an energy per particle smaller than the homogeneous Hartree-Fock ones for r_s>90 and r_s>28, respectively. Moreover, for the polarized case, the energy per particle at r_s=100 is -0.01448ryd close {to -0.0153530(8)ryd, the best quantum Monte Carlo value [Drummond et al., Phys. Rev.B {\bf 69}, 085116, (2004)] and this discrepancy measures the correlation contribution neglected in our approximation.