  We study the thin torus limit of the Haldane-Rezayi state. Eight of the ten
ground states are found to assume a simple product form in this limit, as is
known to be the case for many other quantum Hall trial wave functions. The two
remaining states have a somewhat unusual thin torus limit, where a "broken"
pair of defects forming a singlet is completely delocalized. We derive these
limits from the wave functions on the cylinder, and deduce the dominant matrix
elements of the thin torus hollow-core Hamiltonians. We find that there are
gapless excitations in the thin torus limit. This is in agreement with the
expectation that local Hamiltonians stabilizing wave functions associated with
non-unitary conformal field theories are gapless. We also use the thin torus
analysis to obtain explicit counting formulas for the zero modes of the
hollow-core Hamiltonian on the torus, as well as for the parent Hamiltonians of
several other paired and related quantum Hall states.
