2017/07/31 by Koji Kudo, Toshikaze Kariyado, Yasuhiro Hatsugai
Physics and Astronomy · #Advanced Condensed Matter Physics #Composite fermion #Fermion #Filling factor #Ground state #Landau quantization #Lattice (music) #Quantum Hall effect #Quantum many-body systems #Scaling #Topological Materials and Phenomena #cond-mat.str-el
paper · pdf · doi:10.7566/jpsj.86.103701
published as J. Phys. Soc. Jpn. 86, 103701 (2017) · 4 pages, 3 figures
openalex created_date 2017/07/31 · openalex publication_date 2017/09/04 · arxiv created 2017/09/15 · arxiv updated 2017/09/18 · openalex updated_date 2026/08/05
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, ν=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 ν=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.