Multi-layer fractional quantum Hall states in lattice systems

We study fractional quantum Hall states of interacting particles in lattice systems subject to external magnetic fields. When the number of flux quanta per lattice plaquette 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 pseudospin or layer-index. We find a class of multi-layer fractional quantum Hall states that can form in these systems with different inter- and intra-layer interactions and show that topological and spectral properties of these states can be derived from different conformal field theories that are related by a condensation/orbifolding mechanism.