  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, $\mu_{N}=E(N)-E(N-1)$,
satisfies, $(\mu_{N}+\mu_{N_{\ell}+2-N)}/2 \approx V+2t (N, N_{\ell}, V, E(N)$
and $t$ are the number of electrons, the number of dots, and the strength of
nearest neighbor electron-electron interactions, the total groundstate 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.
