Many-Body Chern Numbers of $\nu =1/3$ and $1/2$ States on Various Lattices

Abstract

For various two dimensional lattices such as honeycomb, kagome, and square-octagon, gauge conventions (string gauge) realizing minimum magnetic fluxes that are consistent with the lattice periodicity are explicitly given. Then many-body interactions of lattice fermions are projected into the Hofstadter bands to form pseudopotentials. By using these pseudopotentials, degenerate many-body ground states are numerically obtained. We further formulate a scheme to calculate the Chern number of the ground state multiplet by the pseudopotentials. For the filling factor of the lowest Landau level, $\nu =1/3$, a simple scaling form of the energy gap are numerially obtained and the ground state is unique except the three-fold topological degeneracy. This is a quantum liquid, which can be lattice analogue of the Laughlin state. For the $\nu =1/2$ case, validity of the composite fermion picture is discussed in relation to the existence of the Fermi surface. Effects of disorder are also described.

4 pages, 3 figures

References in corpus (6)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Fractional quantum Hall states at zero magnetic field
• Fractional quantum Hall effect in the absence of Landau levels
• Composite Fermion Theory for Bosonic Atoms in Optical Lattices
• Particle Entanglement Spectra for Quantum Hall states on Lattices

Cited by in corpus (5)

• Flat band, spin-1 Dirac cone, and Hofstadter diagram in the fermionic square kagome model
• Lieb-Schultz-Mattis theorem in higher dimensions from approximate magnetic translation symmetry
• Adiabatic Heuristic Principle on a Torus and Generalized Streda Formula
• Projectification of point group symmetries with a background flux and Lieb-Schultz-Mattis theorem
• Stability of quasi-particle creation and multiband geometry in fractional Chern insulators under magnetic fields