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 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).