A recent experiment has examined ultracold, fermionic, spin-1/2 ${}^6\mathrm{Li}$ atoms in the Lieb lattice at different Hubbard repulsion $U$ and filling fractions $\nu$ [Lebrat et al., arXiv:2404.17555]. At $\nu =1/2$ and small $U$, they observe an enhanced compressibility on the $p_{x,y}$ sites, pointing to a flat band near the Fermi energy. At $\nu =1/2$ and large $U$ they observe an insulating ferrimagnet. Both small and large $U$ observations at $\nu =1/2$ are consistent with theoretical expectations. Surprisingly, near $\nu =1/4$ and large $U$, they again observe a large $p_{x,y}$ compressibility, pointing to a flat $p_{x,y}$ band of fermions across the Fermi energy. Our Hartree-Fock computations near $\nu =1/4$ find states with canted magnetism (and related spiral states) at large $U$, which possess nearly flat $p_{x,y}$ bands near the Fermi level. We employ parton theories to describe quantum fluctuations of the magnetic order found in Hartree-Fock. We find a metallic state with ${\mathbb{Z}}_2$ fractionalization possessing gapless, fermionic, spinless “chargons” carrying ${\mathbb{Z}}_2$ gauge charges which have a nearly flat $p_{x,y}$ band near their Fermi level: this fractionalized metal is also consistent with observations. Our DMRG study does not indicate the presence of magnetic order, and so is in agreement with a fractionalized ground state. Given the conventional ferrimagnetic insulator at $\nu =1/2$, the ${\mathbb{Z}}_2$ fractionalized metal at $\nu =1/4$ represents a remarkable realization of doping-induced fractionalization.

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• Fractionalization
• Quantum spin liquid
• Ultracold gases
• Hubbard model