Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra

TL;DR

This paper proves that fractional Chern insulators can exist in all topological ideal flatbands with nonzero Chern number, even with nonuniform Berry curvature, by establishing an exact algebraic framework and wavefunction form.

Contribution

It introduces an exact color-entangled wavefunction and density algebra for topological ideal flatbands, demonstrating stability of fractional Chern insulators regardless of Berry curvature uniformity.

Findings

Fractional Chern insulators are stabilized in all topological ideal flatbands with nonzero Chern number.

The authors construct an exact color-entangled wavefunction as a superposition of Landau level states.

The density operator obeys a closed algebra similar to Girvin-MacDonald-Platzman, enabling exact mapping to Landau levels.

Abstract

It is commonly believed that nonuniform Berry curvature destroys the Girvin-MacDonald-Platzman algebra and as a consequence destabilizes fractional Chern insulators. In this work we disprove this common lore by presenting a theory for all topological ideal flatbands with nonzero Chern number C. The smooth single-particle Bloch wavefunction is proved to admit an exact color-entangled form as a superposition of C lowest Landau level type wavefunctions distinguished by boundary conditions. Including repulsive interactions, Abelian and non-Abelian model fractional Chern insulators of Halperin type are stabilized as exact zero-energy ground states no matter how nonuniform Berry curvature is, as long as the quantum geometry is ideal and the repulsion is short-ranged. The key reason behind is the existence of an emergent Hilbert space in which Berry curvature can be exactly flattened by adjusting wavefunction's normalization. In such space, the flatband-projected density operator obeys a closed Girvin-MacDonald-Platzman type algebra, making exact mapping to C-layered Landau levels possible. In the end we discuss applications of the theory to moire flatband systems with a particular focus on the fractionalized phase and spontaneous symmetry breaking phase recently observed in graphene based twisted materials.