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

TL;DR

This paper investigates charge and spin ordering in one-dimensional electron systems with long-range Coulomb interactions, revealing regimes of classical Wigner crystal behavior, charge-density waves, and antiferromagnetic coupling, with implications for organic quasi-1D compounds.

Contribution

It introduces a variational approach to describe quantum Wigner crystals in 1D systems with long-range interactions, analyzing charge and spin orderings across different interaction strengths.

Findings

Identifies three regimes based on Coulomb interaction strength: classical Wigner crystal, continuum-like Wigner crystal, and charge-density wave.

Shows that in the Wigner crystal regime, spins are coupled antiferromagnetically with a smaller energy scale than charge ordering.

Provides insights into the coexistence of magnetic and charge orderings in organic quasi-1D compounds.

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.