  At low temperature, collective excitations of one-dimensional (1D)
interacting fermions exhibit spin-charge separation, a unique feature predicted
by the Tomonaga-Luttinger liquid (TLL) theory, but a rigorous understanding
remains challenging. Using the thermodynamic Bethe Ansatz (TBA) formalism, we
analytically derive universal properties of a 1D repulsive spin-1/2 Fermi gas
with arbitrary interaction strength. We show how spin-charge separation emerges
from the exact TBA formalism, and how it is disrupted by the interplay between
the two degrees of freedom which brings us beyond the TLL paradigm. Based on
the exact low-lying excitation spectra, we further evaluate the spin and charge
dynamical structure factors (DSFs). The peaks of the DSFs exhibit
distinguishable propagating velocities of spin and charge as functions of
interaction strength, which can be observed by Bragg spectroscopy with
ultracold atoms.
