The study of exactly solved models yields significant applications in a wide range of fields in physics and mathematics. In this talk, we first report an observation of quantum criticality and the Luttinger liquid in a system of ultracold 87Rb atoms within 1D tubes. We observe universal scaling laws, characteristic critical temperatures, speed of sound and Wilson ratio of the 1D Bose gas which are in excellent agreements with the results obtained from the theory of Yang-Yang grand canonical ensemble [1]. Moreover, using Takahashi’s spin string hypothesis, we will further discuss the scaling functions of thermal and magnetic properties of the spin-1/2 Heisenberg chain, providing a rigorous understanding of the quantum criticality of spinons. Applying our analytical results we precisely determine the quantum scalings and critical exponents of all magnetic properties in the ideal 1D spin-1/2 antiferromagnet Cu(C4H4N2)(NO3)2 recently studied in [2,3]. Our methods provide a precise understanding of quantum critical phenomena in many-body systems of interacting bosons, fermions and spins.

[1] B. Yang et al. arXiv:1611.00426.
[2] Y. Kono et al. Phys. Rev. Lett. 114, 037202 (2015).
[3] F. He et al. arXiv:1702.05903.