Yang–Yang Equilibrium Statistical Mechanics: A Brilliant Method

Yang and Yang in 1969 [J. Math. Phys. 10, 1115 (1969)] for the first time proposed a rigorous approach to the thermodynamics of the one-dimensional system of bosons with a delta-function interaction. This paper was a breakthrough in exact statistical mechanics, after Yang [Phys. Rev. Lett. 19, 1312 (1967)] published his seminal work on the discovery of the Yang-Baxter equation in 1967. Yang and Yang's brilliant method yields significant applications in a wide range of fields of physics. In this paper, we briefly introduce the method of the Yang-Yang equilibrium statistical mechanics and demonstrate a fundamental application of the Yang-Yang method for the study of thermodynamics of the Lieb-Liniger model with strong and weak interactions in a whole temperature regime. We also consider the equivalence between the Yang-Yang's thermodynamic Bethe ansatz equation and the thermodynamics of the ideal gas with the Haldane's generalized exclusion statistics.