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arXiv · 1707.06722

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

Koji Kudo·Toshikaze Kariyado·Yasuhiro Hatsugai
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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.

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Koji Kudo, Toshikaze Kariyado, Yasuhiro Hatsugai. 2017-07-20. Many-Body Chern Numbers of $\nu=1/3$ and $1/2$ States on Various Lattices. https://doi.org/10.7566/jpsj.86.103701

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