Moire driven edge reconstruction in Fractional quantum anomalous Hall states

We investigate fractional edge modes in moire fractional quantum anomalous Hall states, focusing on the role of lattice momentum conservation and umklapp scattering. For the hierarchical nu=2/3 state, we show that, for a class of microscopic edge realizations, moire-enabled umklapp processes can stabilize the Kane-Fisher-Polchinski fixed point even in the absence of disorder. Our results illustrate how lattice momentum constraints can qualitatively reshape the interaction structure and low-energy behavior of fractional edge modes. The study of Umklapp processes in edge reconstruction serves as a crucial bridge to understanding thermal and electrical transport in the hierarchical fractional quantum anomalous Hall states found in lattice systems of quantum simulators.