Low-density limit of dynamical correlations in the Lieb-Liniger model

Abstract

We derive explicit expressions for dynamical correlations of the field and density operators in the Lieb-Liniger model, within an arbitrary eigenstate with a small particle density $\mathcal{D}$. They are valid for all space and time and any interaction strength $c>0$, and are the leading order of an expansion in $\mathcal{D}$. This expansion is obtained by writing the correlation functions as sums over form factors when formally decomposed into partial fractions.

arXiv comment30 pages

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• Correlation functions and transport coefficients in generalised hydrodynamics
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• Out-of-equilibrium dynamics of the XY spin chain from form factor expansion
• Exact results of dynamical structure factor of Lieb-Liniger model
• The relevant excitations for the one-body function in the Lieb-Liniger model
• One-body dynamical correlation function of Lieb-Liniger model at finite temperature
• Finite temperature single-particle Green's function in the Lieb-Liniger model
• Exact Spectral Function of One-Dimensional Bose Gases