Dynamical structure factor of one-dimensional hard rods

The zero-temperature dynamical structure factor S(q,w) 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,w) 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,w) extends beyond the low-energy limit and confirms a theoretical prediction regarding the behavior of S(q,w) at specific wave vectors Qn=n2π/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 He4 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.