Two-dimensional easy-plane SU$(3)$ magnet with the transverse field: Anisotropy-driven multicriticality

Abstract

The two-dimensional easy-plane SU$(3)$ magnet subjected to the transverse field was investigated with the exact-diagonalization method. So far, as to the $XY$ model (namely, the easy-plane SU$(2)$ magnet), the transverse-field-driven order-disorder phase boundary has been investigated with the exact-diagonalization method, and it was claimed that the end-point singularity (multicriticality) at the $XX$-symmetric point does not accord with large-$N$-theory's prediction. Aiming to reconcile the discrepancy, we extend the internal symmetry to the easy-plane SU$(3)$ with the anisotropy parameter $\eta$, which interpolates the isotropic ($\eta =0$) and fully anisotropic ($\eta =1$) cases smoothly. As a preliminary survey, setting $\eta =1$, we analyze the order-disorder phase transition through resorting to the fidelity susceptibility ${\chi }_F$, which exhibits a pronounced signature for the criticality. Thereby, with $\eta$ scaled carefully, the ${\chi }_F$ data are cast into the crossover-scaling formula so as to determine the crossover exponent $\varphi$, which seems to reflect the extension of the internal symmetry group to SU(3).

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Cited by in corpus (1)

• 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