Few-body route to one-dimensional quantum liquids

Gapless many-body quantum systems in one spatial dimension are universally described by the Luttinger liquid effective theory at low energies. Essentially, only two parameters enter the effective low-energy description, namely, the speed of sound and the Luttinger parameter. These are highly system dependent and their calculation requires accurate nonperturbative solutions of the many-body problem. Here we present a simple theoretical method that only uses collisional information to extract the low-energy properties of spinless one-dimensional systems. Our results are in remarkable agreement with available results for integrable models and from large-scale Monte Carlo simulations of one-dimensional helium and hydrogen isotopes. Moreover, we estimate theoretically the critical point for spinodal decomposition in one-dimensional He-4 and show that the exponent governing the divergence of the Luttinger parameter near the critical point is exactly 1/2, in excellent agreement with Monte Carlo simulations.