One-dimensional liquid $^4$He: dynamical properties beyond Luttinger liquid theory

TL;DR

This paper investigates the dynamical properties of one-dimensional liquid helium-4 at zero temperature, revealing a transition from a critical liquid to a quasi-solid, and providing results beyond traditional Luttinger liquid theory using advanced Quantum Monte Carlo methods.

Contribution

It offers the first comprehensive analysis of dynamical structure factors in 1D liquid $^4$He beyond Luttinger liquid theory, including new analytical relations for the quasi-solid regime.

Findings

Transition from critical liquid to quasi-solid with increasing density

Quantitative results beyond Luttinger liquid theory at higher energies

Observation of fermionic-like particle-hole continuum at higher densities

Abstract

We compute the zero-temperature dynamical structure factor of one-dimensional liquid $^4$He by means of state-of-the-art Quantum Monte Carlo and analytic continuation techniques. By increasing the density, the dynamical structure factor reveals a transition from a highly compressible critical liquid to a quasi-solid regime. In the low-energy limit, the dynamical structure factor can be described by the quantum hydrodynamic Luttinger liquid theory, with a Luttinger parameter spanning all possible values by increasing the density. At higher energies, our approach provides quantitative results beyond the Luttinger liquid theory. In particular, as the density increases, the interplay between dimensionality and interaction makes the dynamical structure factor manifest a pseudo {\it{particle-hole}} continuum typical of fermionic systems. At the low-energy boundary of such region and moderate densities, we find consistency, within statistical uncertainties, with predictions of a power-law structure by the recently-developed non-linear Luttinger liquid theory. In the quasi-solid regime we observe a novel behavior at intermediate momenta, which can be described by new analytical relations that we derive for the hard-rods model.