Fractional Quantum Hall Effect in an Array of Quantum Wires

Abstract

We demonstrate the emergence of the quantum Hall (QH) hierarchy in a 2D model of coupled quantum wires in a perpendicular magnetic field. At commensurate values of the magnetic field, the system can develop instabilities to appropriate interwire electron hopping processes that drive the system into a variety of QH states. Some of the QH states are not included in the Haldane-Halperin hierarchy. In addition, we find operators allowed at any field that lead to novel crystals of Laughlin quasiparticles. We demonstrate that any QH state is the ground state of a Hamiltonian that we explicitly construct.