Kapit_Mueller_Model-> By modifying the hopping term in the Hofstadter Hamiltonian, Kapit and Mueller found an lattice model whose ground-state single particle wavefunctions are lowest Landau level wavefunctions. By adding local repulsive interactions, one can achieve Laughlin wavefunction as many-body ground state, therefore achieving the Fractional Quantum Hall Effect in the lattice. In the code, I reproduced the results of Kapit and Mueller, showing that lowest p-bands collapsing into a single degenerate band. https://arxiv.org/abs/1005.3282

Results_for_Harper_Equation_and_2D_Hamiltonian_Approach-> I reproduce the well-known Hofstadter Butterfly by finding the spectrum of the Hofstadter Hamiltonian using the Harper equation and exact diagonalization of the Hamiltonian under periodic boundary conditions. https://journals.aps.org/prb/abstract/10.1103/PhysRevB.14.2239