  The free fermion nature of interacting spins in one dimensional (1D) spin
chains still lacks a rigorous study. In this letter we show that the length-$1$
spin strings significantly dominate critical properties of spinons, magnons and
free fermions in the 1D antiferromagnetic spin-1/2 chain. Using the Bethe
ansatz solution we analytically calculate exact scaling functions of thermal
and magnetic properties of the model, providing a rigorous understanding of the
quantum criticality of spinons. It turns out that the double peaks in specific
heat elegantly mark two crossover temperatures fanning out from the critical
point, indicating three quantum phases: the Tomonaga-Luttinger liquid (TLL),
quantum critical and fully polarized ferromagnetic phases. For the TLL phase,
the Wilson ratio $R_W=4K_s$ remains almost temperature-independent, here $K_s$
is the Luttinger parameter. Furthermore, applying our results we precisely
determine the quantum scalings and critical exponents of all magnetic
properties in the ideal 1D spin-1/2 antiferromagnet
Cu(C${}_4$H${}_4$N${}_2$)(NO${}_3$)${}_2$ recently studied in Phys. Rev. Lett.
{\bf 114}, 037202 (2015)]. We further find that the magnetization peak used in
experiments is not a good quantity to map out the finite temperature TLL phase
boundary.
