A Geometric Framework in Response to the Call for "Generalized Terms" for Topological States

This work does not aim to derive an effective geometry from a specific Hamiltonian. Instead, it proposes that the geometry is the fundamental organizing principle for a broad class of systems. We construct the simplest, most general geometric framework consistent with the observed phenomenology (competition of scales/potentials) and derive its universal consequences. This approach is analogous to Landau theory, which posits an expansion in an order parameter based on symmetry, not on a microscopic derivation."