Abstract
We calculate the ground state energies and wavefunctions for small systems of interacting fermions on a square lattice with cylindrical topology. We examine the role of next-nearest-neighbour interactions on the observed ground states: the fractional quantum Hall ground state and the super-conducting ground state. Several different probes of fermion-pairing and off-diagonal long-range order as flux quantization, binding energies, pair-correlation functions and critical external magnetic field are investigated. Antiperiodic boundary conditions imposed in one direction provide a test of our numerical results within current size limitations.
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