The ${\mathbb{Z}}_2$-Index of a Pair of Pure States and the Topology of Interacting 1D Superconductors

Anna Mazhar, Jacob Shapiro

We define a relative ${\mathbb{Z}}_2$-index $\mathcal{N}({\omega }_1,{\omega }_2)$ for locally-comparable, parity-invariant pure states on a unital $C^{\ast }$-algebra. We prove that the index is well-def…