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The spectrum of elementary excitations in one-dimensional quantum liquids is determined by ground-state properties. This study reveals exact relations for excitation energy coefficients in Galilean-invariant integrable models.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Systems
  • Low-Dimensional Quantum Systems

Background:

  • Elementary excitations in one-dimensional quantum liquids typically exhibit a linear spectrum at low momenta, characterized by sound velocity.
  • Sound velocity is a key parameter that can be directly related to the system's ground-state energy.

Purpose of the Study:

  • To investigate the spectrum of elementary excitations at higher momenta in Galilean-invariant integrable models.
  • To demonstrate that the excitation spectrum at arbitrary momentum is fully determined by the ground-state properties.
  • To derive general exact relations for excitation energy coefficients and express them using the Luttinger liquid parameter.

Main Methods:

  • Analysis of Galilean-invariant integrable models.
  • Derivation of exact relations for coefficients in the low-momentum expansion of excitation energy.
  • Application of derived formulas to the specific case of the Lieb-Liniger model.

Main Results:

  • The study reveals that the excitation spectrum at arbitrary momentum is completely determined by the ground state properties.
  • General exact relations are found for the coefficients of the low-momentum expansion of excitation energy.
  • These coefficients are expressed in terms of the Luttinger liquid parameter, applicable for arbitrary interactions.

Conclusions:

  • The findings provide a comprehensive understanding of the excitation spectrum in one-dimensional quantum liquids beyond low momenta.
  • The derived exact relations offer new insights into the relationship between ground-state properties and elementary excitations.
  • The application to the Lieb-Liniger model yields novel results, advancing the study of quantum many-body systems.