Canted magnetism and Z₂ fractionalization in metallic states of the Lieb lattice Hubbard model near quarter filling

A recent experiment has examined ultracold, fermionic, spin-1/2 ⁶Li atoms in the Lieb lattice at different Hubbard repulsion U and filling fractions ν (Lebrat et al. 2404.17555). At ν=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 ν=1/2 and large U they observe an insulating ferrimagnet. Both small and large U observations at ν=1/2 are consistent with theoretical expectations. Surprisingly, near ν=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 ν=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 Z₂ fractionalization possessing gapless, fermionic, spinless 'chargons' carrying Z₂ 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 supports a fractionalized ground state. Given the conventional ferrimagnetic insulator at ν=1/2, the Z₂ fractionalized metal at ν=1/4 represents a remarkable realization of doping-induced fractionalization.