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

TL;DR

This paper proposes theoretical models of weakly-coupled spin chains that exhibit spin analogues of superconductivity and the integer quantum Hall effect, enabling dissipationless spin transport.

Contribution

It introduces novel spin-based systems that mimic superconductivity and quantum Hall effects using coupled spin chains, expanding the understanding of topological spin phenomena.

Findings

Mapped spin chain systems to negative-U Hubbard model and quantum Hall systems

Demonstrated potential for dissipationless spin transport in these systems

Provided theoretical framework for spin analogues of topological states

Abstract

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.