On the crystalline states of the dilute jellium model



Strongly localized quantum crystalline states (SLQCS) are determinantal wave-functions made up of the single-particle wave-functions that are obtained from all the distinct crystalline translations of a particular wave-function different from zero only within a primitive cell of the considered crystal and dependent on some parameters α1, ... , αn. The expectation value of the Hamiltonian of the jellium model is numerically evaluated over a class of SLQCS depending on a single parameter α. The minimization of this value with respect to α yields an energy smaller than that of the polarized jellium fluid. The results, compared with the more accurate results obtained by Hartree-Fock and quantum Monte-Carlo procedures, further clarify the importance of the electron localization for the transition to a crystalline phase as well as the localization increase with decreasing density.