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

Abstract

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 $\eta$, there appear a variety of phase boundaries, which meet at the multicritical point $(h,\eta )=(2,0)$. 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 ${\chi }_F$. The fidelity susceptibility does not rely on any presumptions as to the order parameter involved. We made a finite-size-scaling analysis of ${\chi }_F$ for $\eta =1$ (Ising limit), where a number of preceding results are available. Thereby, similar analyses with $\eta$ scaled were carried out around the multicritical point. We found that the ${\chi }_F$ data are described by the crossover scaling theory. A comparison with the preceding studies of the multicriticality is made.

References in corpus (10)

• Dynamics of Loschmidt echoes and fidelity decay
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Cited by in corpus (6)

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• Fidelity-mediated analysis of the transverse-field $XY$ chain with the long-range interactions: Anisotropy-driven multi-criticality
• Longitudinal-field fidelity susceptibility analysis of the $J_1$-$J_2$ transverse-field Ising model around $J_2/J_1\approx 0.5$
• Two-dimensional transverse-field $XY$ model with the in-plane anisotropy and Dzyaloshinskii-Moriya interaction: Anisotropy-driven transition