One-dimensional electron fluid at high density

TL;DR

This study uses variational quantum Monte Carlo to analyze the high-density one-dimensional electron fluid, providing new insights into correlation energy, momentum density, and Tomonaga-Luttinger parameters, with results matching recent high-density theories.

Contribution

First to determine the Tomonaga-Luttinger parameter $K_\rho$ as a function of $r_s$ in the high-density regime for 1D electron fluids.

Findings

Correlation energy fits quadratic in $r_s$

Momentum density exponent used to find $K_\rho$

Results agree with recent high-density theoretical predictions

Abstract

We calculate the ground-state energy, pair correlation function, static structure factor, and momentum density of the one-dimensional electron fluid at high density using variational quantum Monte Carlo simulation. For an infinitely thin cylindrical wire the predicted correlation energy is found to fit nicely with a quadratic function of coupling parameter $r_s$. The extracted exponent $\alpha$ of the momentum density for $k\sim k_F$ is used to determine the Tomonaga-Luttinger parameter $K_\rho$ as a function of $r_s$ in the high-density regime for the first time. We find that the simulated static structure factor and pair correlation function for infinitely thin wires agree with our recent high-density theory [K. Morawetz et al., Phys. Rev. B 97, 155147 (2018)].