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 η, which interpolates the isotropic (η = 0) and fully anisotropic (η = 1) cases smoothly. As a preliminary survey, setting η = 1, we analyze the order–disorder phase transition through resorting to the fidelity susceptibility χ _F, which exhibits a pronounced signature for the criticality. Thereby, with η scaled carefully, the χ _F data are cast into the crossover-scaling formula so as to determine the crossover exponent ϕ, which seems to reflect the extension of the internal symmetry group to SU(3).

用精确对角化方法研究了受横向场作用的二维易平面SU(3)磁体。到目前为止，对于XY模型（即易平面 SU(2) 磁体），已经用精确对角化方法研究了横向场驱动的有序 - 无序相界，并声称最终XX对称点处的点奇异性（多重临界性）与大N理论的预测不符。为了调和这种差异，我们将内部对称性扩展到具有各向异性参数η的易平面 SU(3) ，它插入了各向同性 ( η = 0) 和完全各向异性 ( η= 1) 案件顺利。作为初步调查，设置η = 1，我们通过诉诸保真度敏感性χ _F来分析有序 - 无序相变，其表现出明显的临界特征。因此，通过仔细缩放η，将χ _F数据转换为交叉缩放公式，以确定交叉指数ϕ，这似乎反映了内部对称群对 SU(3) 的扩展。