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

TL;DR

This paper explores magnetic correlations in the finite-doped $SU(3)$ triangular-lattice $t$-$J$ model using neural network variational states, revealing similarities to $SU(2)$ systems and offering insights for quantum simulations.

Contribution

It introduces a neural network-based variational approach to study $SU(3)$ magnetic correlations at finite doping on the triangular lattice, extending understanding beyond previous models.

Findings

Magnetic correlations in $SU(3)$ systems resemble those in $SU(2)$ models.

Enhanced binding energies are observed compared to $SU(2)$ counterparts.

The approach enables analysis of large lattice systems up to $9\times9$.

Abstract

Quantum simulation platforms have become powerful tools for investigating strongly correlated systems beyond the capabilities of classical computation. 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 with dimensions up to $9\times9$ lattice sites 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 binding energies for large periodic systems, and compare our results to the paradigmatic $SU(2)$ square lattice equivalent, finding strikingly similar magnetic correlations, but 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.