2010/10/23 by X-W Guan, X. -W. Guan, Murray T. Batchelor +1 · 31 citations
Mathematics · Physics and Astronomy · #Ansatz #Bethe ansatz #Boson #Cold Atom Physics and Bose-Einstein Condensates #Fermion #Integrable system #Mathematical physics #Mathematics #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Quantum, superfluid, helium dynamics #Scaling #cond-mat.quant-gas
paper · pdf · doi:10.1088/1751-8113/44/10/102001
published in Journal of Physics A Mathematical and Theoretical 44(10), 102001 (Institute of Physics) · 12 pages, 4 figures
arxiv created 2010/10/23 · openalex publication_date 2011/02/16 · arxiv updated 2011/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We demonstrate that the thermodynamics of one-dimensional Lieb–Liniger bosons can be accurately calculated in analytic fashion using the polylog function in the framework of the thermodynamic Bethe ansatz. The approach does away with the need to numerically solve the thermodynamic Bethe ansatz (Yang–Yang) equation. The expression for the equation of state allows the exploration of Tomonaga–Luttinger liquid physics and quantum criticality in an archetypical quantum system. In particular, the low-temperature phase diagram is obtained, along with the scaling functions for the density and compressibility. It has been shown recently by Guan and Ho (arXiv:1010.1301) that such scaling can be used to map out the criticality of ultracold fermionic atoms in experiments. We show here how to map out quantum criticality for Lieb–Liniger bosons. More generally, the polylog function formalism can be applied to a wide range of Bethe ansatz integrable quantum many-body systems which are currently of theoretical and experimental interest, such as strongly interacting multi-component fermions, spinor bosons and mixtures of bosons and fermions.