Linear chain of coupled quantum dots

A linearly coupled chain of spin-polarized quantum dots is investigated under the condition that the number of electrons is equal to or less than the number of the dots. The chemical potential of the system, ${\mu }_N=E\left(N\right)\mathrm{}-E\left(N-1\right),$ satisfies $({\mu }_N+{\mu }_{N_{\mathcal{l}}+2\mathrm{}-N)}/2\mathrm{}\approx V+2t$ $[N,$ $N_{\mathcal{l}},$ $V,$ $E\left(N\right),$ and $t$ are the number of electrons, the number of dots, the strength of nearest-neighbor electron-electron interactions, the total ground-state energy, and the hopping integral between two adjacent dots]. This property will be reflected in the spacing between the conductance peaks. The electron-density structures are determined using a quantum Monte Carlo method. As the number of electrons is varied, several correlated structures are found that are commensurate/incommensurate with the periodic dot system. Hartree-Fock theory fails to predict the correct electronic structures of this system because several nearly degenerate solutions exist.