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Dynamical structure factor of one-dimensional hard rods

The zero-temperature dynamical structure factor $S(q,ω)$ 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, $S(q,ω)$ 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 $S(q,ω)$ extends beyond the low-energy limit and confirms a theoretical prediction regarding the behavior of $S(q,ω)$ at specific wavevectors $\mathcal{Q}_n=n 2 π/a$, 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.