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Motivated by the successful idea of using weakly-coupled quantum electronicwires to realize the quantum Hall effects and the quantum spin Hall effects, wetheoretically construct two systems composed of weakly-coupled quantum spinchains, which can exhibit spin analogues of superconductivity and the integerquantum Hall effect. Specifically, a certain bilayer of two arrays ofinteracting spin chains is mapped, via the Jordan-Wigner transformation, to anegative-$U$ Hubbard model that exhibits superconductivity. In addition, anarray of spin-orbit-coupled spin chains in the presence of an suitable externalmagnetic field is transformed to an array of quantum wires that exhibits theinteger quantum Hall effect. The resultant spin superconductivity and spininteger quantum Hall effect can be characterized by their ability to transportspin without any resistance.

Spin Analogues of Superconductivity and the Integer Quantum Hall Effect in an Array of Spin Chains