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End-point singularity of the XY-paramagnetic phase boundary for the \((2+1)\)D \(S=1\) square-lattice \(J_1\)–\(J_2\) XY model with the single-ion anisotropy

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Abstract

The two-dimensional quantum-spin \(S=1\) square-lattice \(J_1\)–\(J_2\) XY model with the single-ion anisotropy D was investigated numerically, placing an emphasis on the end-point singularity of the phase boundary separating the XY and paramagnetic phases in proximity to the fully frustrated point, \(J_2/J_1 \rightarrow 0.5^{-}\). We employed the exact diagonalization method to circumvent the negative sign problem of the quantum Monte Carlo method, and evaluated the fidelity susceptibility \(\chi _F\) as a probe to detect the phase transition. As a preliminary survey, for an intermediate value of \(J_2/J_1\), the D-driven XY-paramagnetic phase transition was investigated via the probe \(\chi _F\). It turned out that the criticality belongs to the 3D-XY universality class. Thereby, the \(\chi _F\) data were cast into the crossover-scaling formula with the properly scaled distance from the multi-critical point, \(0.5-J_2/J_1\). The set of multi-critical indices was obtained, and compared to those of the quantum Lifshitz criticality.

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Acknowledgements

This work was supported by a Grant-in-Aid for Scientific Research (C) from Japan Society for the Promotion of Science (Grant No. 20K03767).

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  1. Department of Physics, Faculty of Science, Okayama University, Okayama, 700-8530, Japan

    Yoshihiro Nishiyama

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  1. Yoshihiro Nishiyama
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Correspondence to Yoshihiro Nishiyama.

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Nishiyama, Y. End-point singularity of the XY-paramagnetic phase boundary for the \((2+1)\)D \(S=1\) square-lattice \(J_1\)–\(J_2\) XY model with the single-ion anisotropy. Eur. Phys. J. B 96, 96 (2023). https://doi.org/10.1140/epjb/s10051-023-00566-3

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