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arXiv:1608.07722 · Physical Review A

Dynamical structure factor of one-dimensional hard rods

Mário Motta, E. Vitali, M. Rossi, Davide Emilio Galli, Gianluca Bertaina

Published Oct 13, 2016• 31 citations
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Abstract

The zero-temperature dynamical structure factor $S(q,\ensuremath{\omega})$ 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, $S(q,\ensuremath{\omega})$ reveals a crossover from the Tonks-Girardeau gas to a quasisolid regime, along which the low-energy properties are found in agreement with the nonlinear Luttinger liquid theory. Our quantitative estimate of $S(q,\ensuremath{\omega})$ extends beyond the low-energy limit and confirms a theoretical prediction regarding the behavior of $S(q,\ensuremath{\omega})$ at specific wave vectors ${\mathcal{Q}}_{n}=n2\ensuremath{\pi}/a$, 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 $^{4}\mathrm{He}$ 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.

DOI
10.1103/physreva.94.043627

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We investigate zero temperature liquid 4^44He in strictly one dimension by means of state-of-the-art Quantum Monte Carlo and analytic continuation techniques. The system displays the unique feature of spanning all the possible values of the Tomonaga-Luttinger liquid parameter KLK_LKL​ by only changing the density. We explore the behavior of the dynamical structure factor S(q,ω)S(q,\omega)S(q,ω) beyond the limits of applicability of Tomonaga-Luttinger liquid theory in the whole range in KLK_LKL​. We observe a crossover from a weakly interacting Bose gas regime at low density (KL≫1K_L\gg 1KL​≫1) to a quasi-solid regime at high density (KL≪1K_L\ll 1KL​≪1), which we interpret in terms of novel analytical expressions for the spectrum of hard-rods. During this transition the interplay between dimensionality and interaction makes S(q,ω)S(q,\omega)S(q,ω) manifest a pseudo particle-hole continuum typical of a fermionic system, while the Bogoliubov mode evolves into a remnant of the roton mode. We provide also a perturbative estimation of the drag force experienced by a soft impurity moving along the system.
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