Dynamical structure factor of one-dimensional hard rods

TL;DR

This paper computes the dynamical structure factor of one-dimensional hard rods across different densities, revealing a crossover from a Tonks-Girardeau gas to a quasi-solid regime, and confirms theoretical predictions at specific wavevectors.

Contribution

It provides a comprehensive calculation of $S(q,omega)$ for hard rods, extending beyond low-energy limits and connecting with experimental systems like dense 1D quantum liquids.

Findings

Agreement with nonlinear Luttinger liquid theory at low energies

Confirmation of theoretical predictions at specific wavevectors

Similarity between hard rods and dense 1D $^4$He

Abstract

The zero-temperature dynamical structure factor $S(q,\omega)$ of one-dimensional hard rods is computed using state-of-the-art quantum Monte Carlo and analytic continuation techniques, complemented by a Bethe Ansatz analysis. As the density increases, $S(q,\omega)$ reveals a crossover from the Tonks-Girardeau gas to a quasi-solid regime, along which the low-energy properties are found in agreement with the nonlinear Luttinger liquid theory. Our quantitative estimate of $S(q,\omega)$ extends beyond the low-energy limit and confirms a theoretical prediction regarding the behavior of $S(q,\omega)$ at specific wavevectors $\mathcal{Q}_n=n 2 \pi/a$, where $a$ is the core radius, resulting from the interplay of the particle-hole boundaries of suitably rescaled ideal Fermi gases. We observe significant similarities between hard rods and one-dimensional $^4$He at high density, suggesting that the hard-rods model may provide an accurate description of dense one-dimensional liquids of quantum particles interacting through a strongly repulsive, finite-range potential.