  Strong correlation in one-dimensional (1D) quantum systems drastically
changes their dynamic and transport properties in the presence of the
interaction. In this letter, combining quantum integrable theory with numerics,
we exactly compute the spectral function of 1D Lieb-Liniger gas at a many-body
level of large scales. It turns out that a full capture of the power-law
singularities in the vicinities of thresholds requires system size as large as
thousands of particles. Our research essentially confirms the validity of the
nonlinear Tomonaga-Luttinger liquid and provides a reliable technique for
studying critical behaviour emerged only in thermodynamic limit.
