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

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Koji Kudo¹, Toshikaze Kariyado², and Yasuhiro Hatsugai¹^,³

+ Affiliations

¹Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan²International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan³Division of Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan

Received July 20, 2017; Accepted August 3, 2017; Published September 4, 2017

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

https://doi.org/10.7566/JPSJ.86.103701

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

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