Dynamical correlations in one-dimensional 4He beyond Luttinger theory

We study a collection of $^4$He atoms confined to strictly one dimension at zero temperature. We use the exact Path Integral Ground State method to evaluate the equation of state and the radial distribution function, and we find that the system behaves as a Luttinger liquid with parameter $K_L = \hbar \pi \rho / m v$ that takes all the possible values $0