  Motivated by the successful idea of using weakly-coupled quantum electronic
wires to realize the quantum Hall effects and the quantum spin Hall effects, we
theoretically construct two systems composed of weakly-coupled quantum spin
chains, which can exhibit spin analogues of superconductivity and the integer
quantum Hall effect. Specifically, a certain bilayer of two arrays of
interacting spin chains is mapped, via the Jordan-Wigner transformation, to a
negative-$U$ Hubbard model that exhibits superconductivity. In addition, an
array of spin-orbit-coupled spin chains in the presence of an suitable external
magnetic field is transformed to an array of quantum wires that exhibits the
integer quantum Hall effect. The resultant spin superconductivity and spin
integer quantum Hall effect can be characterized by their ability to transport
spin without any resistance.
