Abstract

For a long time, exactly solvable models had been considered to be mathematical toy models. However, such an impression has been drastically changed over the past two decades due to advanced quantum engineering of genuine many-body systems using ultracold atoms and solid material synthesis. In particular, trapping and cooling atoms in one-dimensional (1D) optical waveguides have provided remarkable realisations of exactly solved models in the lab. In turn, exactly solvable Yang–Baxter systems, ranging from the Heisenberg spin chains to the Yang-Gaudin Fermi gas, Hubbard model, Bardeen-Cooper-Schrieffer model and Kondo problems, etc., have provided rigorous understanding of novel many-body phenomena. In this talk, I will briefly review developments of exactly solvable models and describe some of these fundamental mathematical models with the power of quantum integrability. Finally, I will discuss their relevance to recent and future experiments on quantum liquids, quantum criticality, quantum transport and quantum technology, displaying the essence of quantum many-body physics.