Legacy of Yang-Yang Thermodynamics

With this great opportunity to celebrate Professor Yang Chen Ning's 100th birthday, we are very honored to enjoy the modern physics built on the framework drawn by a series of his theories. We have fortunately studied in experiment the quantum criticality and Luttinger liquid with ultracold atoms, which is directly connected to the Yang-Yang thermodynamics. Yang Chen Ning and Yang Chen Ping's seminal work on thermodynamics of the one-dimensional Bose gas with delta-function interaction published in 1969 led to a significant step to treat macroscopic properties of integrable systems in an exact manner. This work has not only provided a profound understanding of a variety of physical phenomena, such as universal thermodynamics, quantum criticality and Luttinger liquids, but also given an impetus for recent developments on generalized hydrodynamics and quantum transport of quantum integrable systems of interacting bosons, fermions and spins. In this brief review, we will recapitulate theoretical and experimental studies of Yang-Yang grand canonical thermodynamics in ultracold atoms inone dimension. In particular, recent novel experimental observations of Luttinger liquids, quantum criticality, magnetism and dynamics will be discussed in terms of quantum integrability.