Sub-dimensional magnetic polarons in the one-hole doped SU(3) $t$-$J$ model

TL;DR

This paper investigates the behavior of a single hole in the SU(3) $t$-$J$ model, revealing sub-dimensional magnetic polarons and complex ground states, with implications for ultracold atom experiments and high-temperature superconductivity.

Contribution

It introduces the concept of sub-dimensional magnetic polarons in the SU(3) $t$-$J$ model and describes their dynamics using geometric string theory, expanding understanding of doped SU(N) systems.

Findings

Magnetic polarons consist of chargons and flavor defects constrained to a single dimension.

Ground states at finite doping may form coupled Luttinger liquids along diagonals.

Results are relevant for quantum gas microscope experiments with ultracold atoms.

Abstract

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 SU(N) spin symmetries, even richer magnetic ground states appear at a filling of one particle per site compared to the case of SU(2) spins, but their fate upon doping remains largely unexplored. Here we address this question by studying a single hole in the SU(3) $t$-$J$ 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 SU(N) 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 SU(N) Fermi-Hubbard models on various geometries.