Graviton modes of Fractional Chern Insulators

We construct an adiabatic crossover from the fractional quantum Hall (FQH) regime to the fractional Chern insulator (FCI) regime. By interpolating between the Hofstadter Hamiltonian and the π-flux checkerboard lattice, we investigate the evolution of the chiral graviton mode (CGM) using exact diagonalization (ED) and density matrix renormalization group (DMRG) techniques. In the FCI phase, the CGM is probed via a chiral quadrupolar density operator. For both the bosonic ν = 1/2 and fermionic ν = 1/3 FCIs, the graviton mode remains adiabatically connected throughout the crossover, though its spectral peak becomes slightly broadened. Remarkably, we observe that increasing interaction strength leads to a rapid decay of the CGM, even when the ground state remains in the FCI phase. This suggests that both band mixing and Landau-level mixing are detrimental to the CGM. Our results provide evidence for the existence of the CGM in lattice realizations of FCIs.