Dispersion of Anyon Bloch Bands

TL;DR

This paper analytically constructs anyon Bloch states in fractional Chern insulators, revealing how quantum geometry and symmetries influence their dispersion, with implications for understanding topological quantum states.

Contribution

It provides an analytical method to compute anyon spectra in ideal bands, linking dispersion to quantum geometry and emergent symmetries, and explains degeneracies in the spectrum.

Findings

Anyon spectrum exhibits m-fold degeneracy from topological properties.

Anyon dispersion bandwidth is controlled by quantum geometry non-uniformity.

Higher harmonics of quantum geometry suppress the anyon dispersion.

Abstract

Fractional Chern insulators (FCIs) are zero magnetic field analogs of fractional quantum Hall states. While the electrons forming an FCI are not subject to an external magnetic field, their anyonic excitations experience a magnetic field with finite-flux due to a many-body Berry phase, whose lattice periodicity generically induces some dispersion. From Laughlin wavefunctions at filling 1/m, we analytically construct single-anyon Bloch states in an ideal band, providing a basis to efficiently compute the dispersion. The anyon spectrum exhibits an $m$-fold degeneracy in the reduced magnetic Brillouin zone (BZ), which originates from the topological degeneracy of the FCI. From our wavefunctions, we derive the m^2-fold degeneracy seen in previous works, showing it to be a splicing of anyon momenta into the electronic BZ. Finally, we find that the anyon dispersion bandwidth is controlled by quantum geometry non-uniformity, growing linearly at weak modulation and saturating at strong modulation. Remarkably, higher harmonics of the quantum geometry alone strongly suppress the dispersion, which we attribute to emergent magnetic translation symmetries. When combined with the first harmonic, a positive (negative) second harmonic drives the system toward a second- (first-) harmonic-dominated regime, thereby reducing (enhancing) the bandwidth. Our results offer an analytically controlled method for evaluating anyon spectra in ideal band FCI, shedding light on how non-uniform quantum geometry and emergent symmetries shape the dispersion of anyons.