Composite Boson Theory of Fractional Chern Insulators

TL;DR

This paper introduces a real-space composite boson framework for understanding fractional Chern insulators, simplifying the many-body problem and unifying lattice and continuum fractional quantum Hall phases.

Contribution

It develops a novel real-space basis and criterion for stable FCIs, validated through numerical evidence, bridging continuum and lattice topological phases.

Findings

Composite boson formation confirmed in Haldane model

Maximizing two-body interaction energy predicts FCI stability

Unified real-space interpretation for quantum Hall phases

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.