On the crystalline states of the dilute jellium model

What is it about?

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.

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Why is it important?

In constructing the determinantal function of the ground crystalline state, the key feature is the use of functions that are non vaninshing only within the unit cell.