Ground-state properties of the one dimensional electron liquid

TL;DR

This paper develops a theoretical framework for understanding the ground-state properties of a one-dimensional electron liquid, including pair distribution functions, effective interactions, and correlation energies, with results aligning well with numerical data.

Contribution

It introduces a zero-energy scattering Schrödinger equation approach combined with the Fermi hypernetted-chain approximation to analyze 1D electron liquids, providing new insights into their correlation functions and spectra.

Findings

Good agreement with diffusion Monte Carlo data for g(z) and S(k)

Accurate calculation of correlation energy and charge excitation spectrum

Qualitative agreement with Luttinger liquid model predictions

Abstract

We present a theory of the pair distribution function $g(z)$ and many-body effective electron-electron interaction for one dimensional (1D) electron liquid. Our approach involves the solution of a zero-energy scattering Schr\"odinger equation for $\sqrt{g(z)}$ where we implemented the Fermi hypernetted-chain approximation including the elementary diagrams corrections. We present numerical results for $g(z)$ and the static structure factor $S(k)$ and obtain good agreement with data from diffusion Monte Carlo studies of the 1D system. We calculate the correlation energy and charge excitation spectrum over an extensive range of electron density. Furthermore, we obtain the static correlations in good qualitative agreement with those calculated for the Luttinger liquid model with long-range interactions.