Subdimensional magnetic polarons in the one-hole doped SU(3) $t\text{−}J$ model

The physics of doped Mott insulators is at the heart of strongly correlated materials and is believed to constitute an essential ingredient for high-temperature superconductivity. In systems with higher $\mathrm{SU}\left(N\right)$ spin symmetries, even richer magnetic ground states appear at a filling of one particle per site compared to the case of $\mathrm{SU}\left(2\right)$ spins, but their fate upon doping remains largely unexplored. Here we address this question by studying a single hole in the SU(3) $t\text{−}J$ model whose undoped ground state features long-range, diagonal spin stripes. By analyzing both ground-state and dynamical properties utilizing the density matrix renormalization group, we establish the appearence of magnetic polarons consisting of chargons and flavor defects whose dynamics is constrained to a single effective dimension along the ordered diagonal. We semi-analytically describe the system using geometric string theory, where paths of hole motion are the fundamental degrees of freedom. With recent advances in the realization and control of $\mathrm{SU}\left(N\right)$ Fermi-Hubbard models with ultracold atoms in optical lattices, our results can directly be observed in quantum gas microscopes with single-site resolution. Our work suggests the appearance of intricate ground states at finite doping constituted by emergent, coupled Luttinger liquids along diagonals, and is a first step towards exploring a wealth of physics in doped $\mathrm{SU}\left(N\right)$ Fermi-Hubbard models on various geometries.