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We study a system of electrons interacting through long--range Coulomb forceson a one--dimensional lattice, by means of a variational ansatz which is thestrong--coupling counterpart of the Gutzwiller wave function. Our aim is todescribe the quantum analogue of Hubbard's classical ``generalized Wignercrystal''. We first analyse charge ordering in a system of spinless fermions,with particular attention to the effects of lattice commensurability. We arguethat for a general (rational) number of electrons per site $n$ there are threeregimes, depending on the relative strength $V$ of the long--range Coulombinteraction (as compared to the hopping amplitude $t$). For very large $V$ thequantum ground state differs little from Hubbard's classical solution, forintermediate to large values of $V$ we recover essentially the Wigner crystalof the continuum model, and for small $V$ the charge modulation amounts to asmall--amplitude charge--density wave. We then include the spin degrees offreedom and show that in the Wigner crystal regimes (i.e. for large $V$) theyare coupled by an antiferromagnetic kinetic exchange $J$, which turns out to besmaller than the energy scale governing the charge degrees of freedom. Ourresults shed new light on the insulating phases of organic quasi--1D compoundswhere the long--range part of the interaction is unscreened, and magnetic andcharge orderings coexist at low temperatures.Comment: 11 pages, 7 figures, accepted for publication on Phys. Rev.

Charge and spin order in one-dimensional electron systems with long-range Coulomb interactions