The Fractional Quantum Hall effect revealed new phases of matter beyond traditional paradigms, characterized by ground state degeneracy, nontrivial particle statistics, and gapless edge excitations, making them promising for fault-tolerant quantum computation. Determining the topological phase from a microscopic Hamiltonian is challenging, as it often assumes the ground state contains all topological information. It is proposed that topological data can be extract from ground-state wavefunction overlaps, however, this method was impractical for lattice systems. This issue was addressed by constructing specific operators and managing phase factors, applying Wen’s results to lattice systems.
