Ground-state order in magic-angle graphene at filling =-3: A full-scale density matrix renormalization group study

We investigate twisted bilayer graphene (TBG) at filling v = -3 in the presence of realistic heterostrain. Strain amplifies the band dispersion and drives the system beyond the strong-coupling regime of previous theoretical studies. We use DMRG to conduct an unbiased, large-scale numerical calculations that include all spin and valley degrees of freedom, up to bond dimension x = 24 576. We establish a global phase diagram that unifies a number of theoretical and experimental results. Near zero strain we find an intervalley-coherent quantized anomalous Hall (QAH-IVC) state, a competitive strong-coupling order that evaded past numerical studies. A tiny strain around 0.05% drives a transition into an incommensurate Kekule spiral (IKS) phase, supporting the mean-field prediction in [Kwan et al., Phys. Rev. X 11, 041063 (2021)]. Even higher strains above 0.2% favor a flavor-symmetric metallic order, which may explain metals found at v = -3 in many experiments.