Few-particle dynamics of fractional quantum Hall lattice models

TL;DR

This paper investigates the dynamics of particles in lattice models designed for fractional quantum Hall states, revealing fundamental differences from fractional Chern insulators and identifying chiral orbital dynamics.

Contribution

It demonstrates that these lattice Hamiltonians do not behave as interacting particles in Chern bands, providing new insights into their spectral and dynamical properties.

Findings

Single-particle spectrum consists of localized shell states with energy-dependent radii.

Particles exhibit chiral dynamics along well-defined orbits.

The models differ fundamentally from fractional Chern insulators.

Abstract

Considering lattice Hamiltonians designed using conformal field theory to have fractional quantum Hall states as ground states, we study the dynamics of one or two particles on such lattices. Examining the eigenspectrum and dynamics of the single-particle sector, we demonstrate that these Hamiltonians cannot be regarded as describing interacting particles placed on a Chern band, so that the physics is fundamentally different from fractional Chern insulators. The single-particle spectrum is shown to consist of eigenstates localized in shells which have larger radius for larger eigenenergies. This leads to chiral dynamics along reasonably well-defined orbits, both in the single-particle and in the two-particle sectors.