From Ferrimagnetic Insulator to superconducting Luther-Emery Liquid: A DMRG Study of the Two-Leg Lieb Lattice

Motivated by recent experiments on ultracold fermionic spin-1/2 $^6$Li atoms in a Lieb lattice at various Hubbard repulsion $U$ and filling fractions $n$ (Lebrat et al., arXiv:2404.17555), we conduct a density matrix renormalization group (DMRG) analysis of the Hubbard model on a two-leg Lieb ladder. At half-filling, we find a ferrimagnetic Mott insulating ground state, consistent with Lieb's theorem. Away from half-filling, a state with finite total spin $\vec{S}^2 \neq 0$ and vanishing charge gap persists down to filling $n_c \approx 2/3$. For lower, incommensurate fillings, the system is described by a Luttinger liquid with one charge and one spin mode. Intriguingly, in a narrow window near $n_c = 2/3$, close to the onset of ferromagnetic order, we identify a superconducting Luther-Emery phase with dominant $s_{xy}$-wave pairing.