Dynamical structure factor of one-dimensional hard rods

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 ${\mathcal{Q}}_n=n2\pi /a$, 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.

13 pages, 9 figures

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• Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution
• Statistical and computational intelligence approach to analytic continuation in Quantum Monte Carlo
• Geometrizing non-relativistic bilinear deformations
• Visualizing the BEC-BCS crossover in the two-dimensional Fermi gas: pairing gaps and dynamical response functions from ab initio computations
• Quantum Critical Behavior of One-Dimensional Soft Bosons in the Continuum
• Beyond-Luttinger-Liquid thermodynamics of a one-dimensional contact repulsive Bose gas
• Analytic thermodynamic properties of the Lieb-Liniger gas
• Correlation properties of a one-dimensional repulsive Bose gas at finite temperature
• Experimental Realization of One Dimensional Helium
• Nonequilibrium scenarios in cluster-forming quantum lattice models
• Dynamical structure factor of a fermionic supersolid on an optical lattice
• Microscopic study of static and dynamical properties of dilute one-dimensional soft bosons
• Emergence of an Ising critical regime in the clustering of 1D soft matter revealed through string variables
• Static density response of one-dimensional soft bosons across the clustering transition
• Evolution of static and dynamical density correlations in a one-dimensional soft-core gas from the Tonks-Girardeau limit to a clustering fluid
• Linear response of one-dimensional liquid ${}^4$He to external perturbations
• Thermodynamics and Tomonaga-Luttinger liquid behavior of the quantum 1D hard rod model
• Dynamic structure factor of quantum hard rods from exact form-factors
• Hole-induced anomaly in the thermodynamic behavior of a one-dimensional Bose gas