Magnetic correlations in the $SU(3)$ triangular-lattice $t$-$J$ model at finite doping

Abstract

Ultracold alkaline-earth atoms and molecules now enable experimental realizations of SU(N)-symmetric Fermi-Hubbard models, yet theoretical understanding of these systems, particularly at finite doping remains limited. Here we investigate the strong-coupling limit of the $SU(3)$ symmetric Fermi-Hubbard model on the triangular lattice across the full doping range. Using a three-flavor extension of Gutzwiller-projected hidden fermion determinant states (G-HFDS), a neural network based variational ansatz, we analyze two- and three-point spin-spin and spin-spin-hole correlations of the $SU(3)$ Cartan generators. We further study the structure of a pair of doped holes for large periodic systems, and compare our results to the paradigmatic $SU(2)$ square lattice equivalent, finding strikingly similar magnetic correlations, non-s-wave pairing symmetry, and enhanced binding energies. Our results provide a foundation for future exploration of doped SU(N) Mott insulators, providing valuable insights for both theoretical developments and quantum simulation experiments.