Stabilizing Fractional Chern States in Twisted MoTe2: Multi-band Correlations via Non-perturbative Renormalization Group

Abstract: The observation of fraction quantum Hall states in twisted MoTe2 has sparked a lof of interest in this phenomenon. Most theoretical works to date rely on the brute-force exact diagonalization which is limited to the one partially occupied band. In this work, we present strong evidence that the effect of higher lying bands cannot be ignored due to strong interband interactions. To tackle these effects, we introduce a non-perturbative driven similarity renormalization group (DSRG) method, originally developed for problems in quantum chemistry. We apply this methodology to twisted MoTe2 at fractional hole fillings of ν = 1/3 and 2/3 across a spectrum of twist angles. Our results show that at ν = 1/3, the many-body excitation energy gaps are substantially reduced compared to the one-band treatment. For ν = 2/3, we find that the dynamic correlations stemming from interband interactions stabilize fractional Chern insulating phases at larger twist angles, consistent with the experimental findings. By examining the correlated orbitals and their single-particle topological features, we demonstrate that this stabilization at higher twist angles arises predominantly from the dynamic correlations, rather than conditions on the single-particle quantum geometric tensor.