Charge and spin order in one dimensional systems with long range Coulomb interaction

Amir Hossein Talebi, B. Davoudi

Tadahiro Miyao, Seigo Okida, Hayato Tominaga

A new framework for the reflection positivity, based on order-preserving operator inequalities, is proposed. This framework is utilized to investigate one-dimensional fermion–phonon systems, with a particular focus on the detailed examination of ground state properties. Our analysis reveals that the reflection positivity provides a consistent description of the charge-density-wave (CDW) order in such systems. Additionally, we establish the existence of CDW long-range order in the ground state when the Coulomb interaction is long range.

Amir Hossein Talebi, B. Davoudi, M. Reza Rahimitabar

H. Maurey, Thierry Giamarchi

One-dimensional electron systems interacting with long-range Coulomb forces (quantum wires) show a Wigner crystal structure. We investigate in this paper the transport properties of such a Wigner crystal in the presence of impurities. Contrary to what happens when only short-range interactions are included, the system is dominated by 4${\mathit{k}}_{\mathit{F}}$ scattering on the impurities. There are two important length scales in such a problem: one is the pinning length above which the (quasi-)long-range order of the Wigner crystal is destroyed by disorder. The other length, ${\ensuremath{\xi}}_{\mathrm{cr}}$, is the length below which Coulomb interactions are not important and the system is behaving as a standard Luttinger liquid with short-range interactions. We obtain the frequency and temperature dependence of the conductivity. We show that such a system is very similar to a classical charge density wave pinned by impurities, but with important differences due to quantum fluctuations and long-range Coulomb interactions. Finally, we discuss our results in comparison with experimental systems.

Alfred Gold, L. Calmels

Using ground-state energy calculations we calculate the density and width dependence of the spin susceptibility and the compressibility of the one-dimensional electron gas with long-range Coulomb interaction. An oscillator potential is used for the confinement. With the compressibility and the spin-susceptibility sum rule we describe charge-density and spin-density excitations in quantum wires as a function of the electron density and the wire-width parameter. Analytical results are presented.

Thomas L. Schmidt