Composite Boson Theory of Fractional Chern Insulators

Abstract: The understanding of fractional Chern insulators (FCIs) has been deeply guided by band topology and quantum geometry. Here, we introduce a real-space theoretical framework in which FCIs are understood in terms of composite bosons, local objects consisting of electrons bound to their energetically excluded surrounding orbitals. The central element of our framework is the construction of a radially ordered set of maximally localized basis for Chern bands without requiring continuous rotational symmetry. Within this basis, the complex many-body problem simplifies to a real-space organizing principle: a stable FCI occurs if the orbitals excluded around central electrons are those maximizing the two-body interaction energy. We validate this with direct numerical evidence for composite boson formation in the Haldane model, demonstrating that our criterion reliably characterizes FCIs. Importantly, our analysis illustrates that the composite boson framework bridges the fractional quantum Hall effect in continuum and lattice paradigms, providing a unified and intuitive real-space interpretation for distinct correlated phases. It thus establishes a foundation for diagnosing and guiding the design of both Abelian and non-Abelian topologically ordered phases across distinct platforms.