Interacting ground states of moiré ladders
Phys. Rev. B 113, 104432 – Published 17 March, 2026
DOI: https://doi.org/10.1103/8lz4-s1f9
Abstract
Moiré materials have emerged as a rich platform for exploring strong correlation effects in low dimensions, with twisted bilayer graphene (TBG) as a paradigmatic example. To distill the essential ingredients driving moiré-induced phases, a simplified one-dimensional analog—a two-leg ladder with spatially modulated interleg hopping and a uniform magnetic flux—was recently introduced. This model, which we refer to as the moiré ladder, features a nearly flat lowest-energy band in a suitable parameter regime, capturing the band-flattening mechanism of TBG. We investigate the ground-state phase diagram of the moiré ladder using a combination of bosonization and density matrix renormalization group techniques, and we systematically disentangle the respective roles of the flux and the hopping modulation. At half-filling, previous numerical work identified a metal-insulator transition at finite interaction strength and an unexpected ferromagnetic ground state. Revisiting this, we show that the metal-insulator transition can be understood perturbatively within bosonization, governed by the number of Fermi points. In contrast, the ferromagnetic correlations are nonperturbative and require both flux and spatial modulation—neither alone is sufficient. We extend our analysis to other fillings: one-quarter, three-quarters, slightly above half-filling (half-filling plus two electrons), and slightly below half-filling (half-filling minus two electrons). At moderate interactions, we observe ferromagnetism below half-filling and antiferromagnetism above; at stronger interactions, ferromagnetism dominates across all studied fillings. Reducing the interaction strength relative to the bandwidth induces a transition back to antiferromagnetic behavior. These results reveal a robust and unconventional mechanism for one-dimensional ferromagnetism rooted in moiré band-structure effects and establish the moiré ladder as a minimal model for probing correlation-driven phases in moiré systems. Crucially, the analysis demonstrates that periodic interleg hopping alone does not engender new correlated phases; the magnetic flux is essential for the observed unconventional behavior.
