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

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

2003-02-03

arxiv.org/abs/cond-mat/0302020v2

Physics

Condensed Matter

Strongly Correlated Electrons

11 pages, 7 figures, accepted for publication on Phys. Rev. B

Scientific paper

10.1103/PhysRevB.68.045112

We study a system of electrons interacting through long--range Coulomb forces on a one--dimensional lattice, by means of a variational ansatz which is the strong--coupling counterpart of the Gutzwiller wave function. Our aim is to describe the quantum analogue of Hubbard's classical ``generalized Wigner crystal''. We first analyse charge ordering in a system of spinless fermions, with particular attention to the effects of lattice commensurability. We argue that for a general (rational) number of electrons per site $n$ there are three regimes, depending on the relative strength $V$ of the long--range Coulomb interaction (as compared to the hopping amplitude $t$). For very large $V$ the quantum ground state differs little from Hubbard's classical solution, for intermediate to large values of $V$ we recover essentially the Wigner crystal of the continuum model, and for small $V$ the charge modulation amounts to a small--amplitude charge--density wave. We then include the spin degrees of freedom and show that in the Wigner crystal regimes (i.e. for large $V$) they are coupled by an antiferromagnetic kinetic exchange $J$, which turns out to be smaller than the energy scale governing the charge degrees of freedom. Our results shed new light on the insulating phases of organic quasi--1D compounds where the long--range part of the interaction is unscreened, and magnetic and charge orderings coexist at low temperatures.

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