| We study fractional quantum Hall states of interacting particles in lattice systems subject to external magnetic fields. When flux density is close to a rational fraction, the lowest energy states can be mapped to degenerate lowest Landau levels in the continuum where particles carry an extra degree of freedom - a layer index or pseudospin. We classify the possible multi-component fractional quantum Hall states that can form in these systems and show that topological properties of quasihole excitations of these states can be derived using different conformal field theories that are related by an orbifold construction. |
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