Kitaev chain with a fractional twist

The topological nontriviality of insulating phases matter are by now well understood through K theory where the indices Dirac operators assembled into classes. We consider in context Kitaev chain a notion generalized operator associated Clifford algebra is centrally extended. demonstrate that central extension achieved via taking rational powers Pauli matrices appear corresponding BdG Hamiltonian. Doing so introduces pseudometallic component to phase diagram within which winding number valued $\mathbb{Q}$. find this hosts mode remains extended presence weak disorder, motivating interpretation nonintegral number. remark correspondence with recent paper demonstrating projective defined absence ${\mathrm{spin}}^{\mathbb{C}}$ structure have indices.