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Local Properties of the Rapidity Distribution in the Lieb-Liniger Model.

Miłosz Panfil1, Zoran Ristivojevic2

  • 1University of Warsaw, Faculty of Physics, Pasteura 5, 02-093 Warsaw, Poland.

Physical Review Letters
|July 31, 2025
PubMed
Summary

We derived exact relations for the Lieb-Liniger model

Area of Science:

  • Quantum many-body physics
  • Condensed matter theory

Background:

  • The Lieb-Liniger model describes interacting one-dimensional Bose gases.
  • Low-temperature properties are crucial for understanding quantum systems.

Purpose of the Study:

  • To analytically determine the free energy of the Lieb-Liniger model at low temperatures.
  • To investigate corrections to existing conformal field theory results.

Main Methods:

  • Derivation of exact relations for rapidity distribution derivatives at the Fermi level.
  • Analytical treatment of free energy at low temperatures and arbitrary interactions.
  • Calculation of leading-order corrections beyond conformal field theory.

Main Results:

  • Identified a new term in the free energy, controlled by a dimensionless parameter.

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  • Calculated series expansions for weak and strong interaction limits.
  • Extended results to other Galilean-invariant integrable systems.

    • Conclusions:

    • The study provides a more accurate analytical description of the Lieb-Liniger model.
    • Introduced a new parameter that characterizes system behavior.
    • The framework is applicable to a broader class of quantum systems.