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

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          Abstract

          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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          Ground state of the two-dimensional electron gas

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            Effects of the electron interaction on the energy levels of electrons in metals

            E. Wigner (1938)
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              Wigner Crystal in One Dimension

              A one--dimensional gas of electrons interacting with long--range Coulomb forces (\(V(r) \approx 1/r\)) is investigated. The excitation spectrum consists of separate collective charge and spin modes, with the charge excitation energies in agreement with RPA calculations. For arbitrarily weak Coulomb repulsion density correlations at wavevector \(4k_F\) decay extremely slowly and are best described as those of a one--dimensional Wigner crystal. Pinning of the Wigner crystal then leads to the nonlinear transport properties characteristic of CDW. The results allow a consistent interpretation of the plasmon and spin excitations observed in one--dimensional semiconductor structures, and suggest an interpretation of some of the observed features in terms of ``spinons''. A possible explanation for nonlinear transport phenomena is given.
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                Author and article information

                Journal
                03 February 2003
                2003-04-29
                Article
                10.1103/PhysRevB.68.045112
                cond-mat/0302020
                72a323a1-f53b-445d-8a59-7374c1a7f61c
                History
                Custom metadata
                11 pages, 7 figures, accepted for publication on Phys. Rev. B
                cond-mat.str-el

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