Recently, new trends in computation, such as artificial intelligence, machine learning and quantum computation are attracting 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 data compression. For example, we developed a flat-band frustrated boson system whose ground state can be mathematically related to the loop gas model. We showed by Monte Calro simulation that its quantum phase transition belongs to the same universality class as the classical XY model.

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