Strongly localized quantum crystalline states and behavior of the dilute jellium model

TL;DR

This paper introduces strongly localized quantum crystalline states (SLQCS) to model dilute quantum crystals, showing their energy behavior and electron confinement properties at low densities in the jellium model.

Contribution

The paper proposes SLQCS as a new wave-function approach for dilute quantum crystals, accurately capturing their low-density behavior and energy scaling.

Findings

SLQCS energy per particle scales as -M_{dl,σ}/r_s + C_{σ}/r_s^{3/2} at large dilution.

M_{dl,σ} corresponds to the Madelung constant for cubic symmetry σ.

Electrons become increasingly confined to cell centers as density decreases.

Abstract

We name strongly localized quantum crystalline state (SLQCS) a determinantal wave-function of the single-particle wave-functions obtained by crystalline translations of a wave-function different from zero only within a primitive cell of the considered quantum crystalline phase. SLQCSs accurately reproduce the low density behaviour of the quantum crystals that, as Wigner's crystalline phase of the jellium model, can become very dilute. Our analysis explicitly deals with this system. We show that the SLQCS energy per particle at large dilution ($r_s$) behaves as $-M_{dl,\sigma}/r_s+C_{\sigma}/{r_s}^{3/2}$, where $M_{dl,\sigma}$ turns out to be the Madelung constant of the considered cubic symmetry $\sigma$ and $C_{\sigma}$ is a positive constant only numerically determined. Moreover, as the density gets smaller and smaller, each electron becomes more and more confined to the centre of its cell.