How Similar Can Fractional Chern Insulators and Fractional Quantum Hall States Be? — Extending Ground-State Correspondence to the Excitation Spectrum

While it is well established that fractional Chern insulators (FCIs) and fractional quantum Hall (FQH) states share identical ground-state topological order, their excitation spectra are generally distinct. Here, we construct a new class of moiré flat Chern bands, substantially different from Landau levels. Remarkably, we find that the many-body spectra of FCI states in these moiré flat bands are nearly indistinguishable from their FQH counterparts. This finding extends the FCI–FQH correspondence beyond the ground state to the excitation spectrum. Our results demonstrate that FCIs can, in principle, reproduce the full phenomenology of the FQH effect.