Multicritical behavior of the fidelity susceptibility for the 2D quantum transverse-field XY model

The two-dimensional quantum XY model with a transverse magnetic field was investigated with the exact diagonalization method. Upon turning on the magnetic field h and the XY -plane anisotropy η, there appear a variety of phase boundaries, which meet at the multicritical point (h, η) = (2, 0). We devote ourselves to the Ising-universality branch, placing an emphasis on the multicritical behavior. As a probe to detect the underlying phase transitions, we adopt the fidelity susceptibility χ_F. The fidelity susceptibility does not rely on any presumptions as to the order parameter involved. We made a finite-size-scaling analysis of χ_F for η = 1 (Ising limit), where a number of preceding results are available. Thereby, similar analyses with η scaled were carried out around the multicritical point. We found that the χ_F data are described by the crossover scaling theory. A comparison with the preceding studies of the multicriticality is made. Graphical abstract:

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