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We use the Fortuin-Kasteleyn representation based improved estimator of thecorrelation configuration as an alternative to the ordinary correlationconfiguration in the machine-learning study of the phase classification of spinmodels. The phases of classical spin models are classified using the improvedestimators, and the method is also applied to the quantum Monte Carlosimulation using the loop algorithm. We analyze theBerezinskii-Kosterlitz-Thouless (BKT) transition of the spin 1/2 quantum XYmodel on the square lattice. We classify the BKT phase and the paramagneticphase of the quantum XY model using the machine-learning approach. We show thatthe classification of the quantum XY model can be performed by using thetraining data of the classical XY model.

Machine-Learning Study using Improved Correlation Configuration and Application to Quantum Monte Carlo Simulation