Few-Body Route to One-Dimensional Quantum Liquids

Abstract

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 non-perturbative solutions of the many-body problem. Here, we present a simple method that only uses collisional information to extract the low-energy properties of these 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 helium-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.

arXiv comment8 pages, 6 figures, including supplementary material

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Cited by in corpus (7)

• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Bose-Fermi dualities for arbitrary one-dimensional quantum systems in the universal low energy regime
• Thermodynamic behavior of a one-dimensional Bose gas at low temperature
• Observation of photon droplets and their dynamics
• Self-bound droplets of light with orbital angular momentum
• Universality and tails of long range interactions in one dimension
• From few to many body degrees of freedom