Critical Properties of One-Dimensional Electron Systems with $1/r^{\alpha}$-type Long-Range Interactions

TL;DR

This paper investigates the critical behavior of one-dimensional electron systems with long-range interactions, revealing a crossover from Luttinger liquid to Wigner crystal and analyzing Fermi-edge singularities influenced by core-hole dynamics.

Contribution

It provides a detailed analysis of the crossover from Tomonaga-Luttinger liquid to Wigner crystal in 1D systems with $1/r^{eta}$ interactions using bosonization.

Findings

Crossover from Luttinger liquid to Wigner crystal as $eta o 1$

Suppression of core-hole motion effects on Fermi-edge singularity near Wigner crystal

Critical behavior dominated by impurity forward-scattering in static hole regime

Abstract

We study the critical properties of one-dimensional electron systems with the $1/r^{\alpha}$-type long-range interaction ($\alpha \ge 1$). Using bosonization methods, we discuss how the 1D system exhibits a crossover from the Tomonaga-Luttinger liquid to the Wigner crystal when $\alpha \to 1$. In particular, a detailed analysis is given to the Fermi-edge singularity phenomena when a {\it mobile} core hole is created suddenly in the valence band. It is found that the effect due to the core-hole motion on the Fermi-edge singularity is gradually suppressed as the system approaches the Wigner crystal, and its critical behavior is dominated by the ordinary impurity forward-scattering inherent in a static hole.