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

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.

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

References in corpus (2)

• The ferroelectric Mott-Hubbard phase of organic (TMTTF)2X conductors
• Quantum Phase Transitions to Charge Order and Wigner Crystal Under Interplay of Lattice Commensurability and Long-Range Coulomb Interaction

Cited by in corpus (24)

• Ground state properties of the one dimensional Coulomb gas
• Charge instabilities and topological phases in the extended Hubbard model on the honeycomb lattice with enlarged unit cell
• Interaction-range effects for fermions in one dimension
• Domain-wall excitons and optical conductivity in one-dimensional Wigner lattices
• Unconventional metallic conduction in two-dimensional Hubbard-Wigner lattices
• Dielectric catastrophe at the magnetic field induced insulator to metal transition in Pr1-xCaxMnO3 (x=0.30, 0.37) crystals
• Variational study of the interacting spinless Su-Schrieffer-Heeger model
• dc conductivity as a geometric phase
• Effects of energy extensivity on the quantum phases of long-range interacting systems
• Dependence of structure factor and correlation energy on the width of electron wires
• One-dimensional electron fluid at high density
• Wigner crystallization of electrons in a one-dimensional lattice: a condensation in the space of states
• Optical and spectral properties of quantum domain-walls in the generalized Wigner lattice
• Fractional charges and spin-charge separation in one-dimensional Wigner lattices
• Long-range interaction in an open boundary-driven Heisenberg spin lattice: A far-from-equilibrium transition to ballistic transport
• Phase diagram of two-component dipolar fermions in one-dimensional optical lattices
• Many-Body Physics in Small Systems: Observing the Onset and Saturation of Correlation in Linear Atomic Chains
• Quantum quench in 2D using the variational Baeriswyl wavefunction
• Enhancement of Wigner crystallization in quasi low-dimensional solids
• Strong Coulomb effects in hole-doped Heisenberg chains
• Magnetism of one-dimensional Wigner lattices and its impact on charge order
• Adiabatic continuity and broken symmetry in many-electron systems: a variational perspective
• Fermion quartets on the square lattice
• Second-order electronic correlation effects in a one-dimensional metal