2016/07/28 by Manuel Valiente, Patrik Öhberg, Patrik Ohberg · 8 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Critical exponent #Critical point (mathematics) #Exponent #Integrable system #Luttinger liquid #Mathematical physics #Mathematics #Monte Carlo method #Phase transition #Physics #Quantum #Quantum Monte Carlo #Quantum many-body systems #Quantum mechanics #Quantum, superfluid, helium dynamics #Spinodal #Statistical physics #cond-mat.quant-gas
paper · pdf · doi:10.1103/physreva.94.051606
published in Physical Review A 94(5) (American Physical Society) · 8 pages, 6 figures, including supplementary material
arxiv created 2016/07/28 · openalex publication_date 2016/11/29 · arxiv updated 2016/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 4He 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.