Recently, the trend of artificial intelligence / machine learning / quantum computation has attracted social attention. Our research group tries to clarify the mathematical core of the methods of computational physics and computational statistical mechanics. We are conducting research based on the development of new methods. As its application, we are elucidating unsolved problems in statistical mechanics and performing comparative calculations with experimental studies in strongly correlated quantum systems in which interactions dominate physical properties. The quantum Monte Carlo and tensor network methods used here are closely related to data science through Boltzmann machines and information compression. An example of recent research is the discovery of a simple representation of the wave function of the Kitaev spin liquid state. In the pursuit of expressing the ground state of the Kitaev model by using a tensor network with as little information as possible, recently, we found that it can be essentially expressed by the loop gas model, a model of classical statistical mechanics.

Classical loop-gas at criticality represents the gapless Kitaev spin liquid.

Abelian and non-Abelian chiral spin liquids in a compact tensor network: H.-Y. Lee, R. Kaneko, T. Okubo and N. Kawashima, Phys. Rev. B101 (2020) 035140.

Boundary conformal spectrum and surface critical behavior of classical spin systems:A tensor network renormalization study: S. Iino, S. Morita and N. Kawashima, Phys. Rev. B101 (2020) 155418.

Magnetic field induced quantum phases in a tensor network study of Kitaev magnets: H.-Y. Lee, R. Kaneko, L. E. Chern, T. Okubo, Y. Yamaji and N. K. &. Y. B. Kim, Nature Communications11 (2020) 1639.

Magnetic field induced competing phases in spin-orbital entangled Kitaev magnets: L. E. Chern, R. Kaneko, H.-Y. Lee and Y. B. Kim, Phys. Rev. Research2 (2020) 013014.