Ground state properties of the one-dimensional electron liquid

TL;DR

This paper uses quantum Monte Carlo methods to analyze the ground state properties of a one-dimensional electron liquid, revealing how interactions influence structure factors, momentum density, and Luttinger liquid behavior.

Contribution

It provides detailed calculations of various properties of the 1D electron gas and demonstrates the impact of interactions on the Fermi wave vector and Luttinger liquid exponents.

Findings

Peaks in the static structure factor grow with increased coupling.

Effective Fermi wave vector increases with interaction strength.

Good agreement of Luttinger liquid exponent with theoretical predictions.

Abstract

We present calculations of the energy, pair correlation function (PCF), static structure factor (SSF), and momentum density (MD) for the one-dimensional electron gas using the quantum Monte Carlo method. We are able to resolve peaks in the SSF at even-integer-multiples of the Fermi wave vector, which grow as the coupling is increased. Our MD results show an increase in the effective Fermi wave vector as the interaction strength is raised in the paramagnetic harmonic wire; this appears to be a result of the vanishing difference between the wave functions of the paramagnetic and ferromagnetic systems. We have extracted the Luttinger liquid exponent from our MDs by fitting to data around the Fermi wave vector, finding good agreement between the exponent of the ferromagnetic infinitely-thin wire and the ferromagnetic harmonic wire.