Griffiths effects and quantum critical points in dirty superconductors without spin-rotation invariance: One-dimensional examples - art. no. 224204

We introduce a strong-disorder renormalization group (RG) approach suitable for investigating the quasiparticle excitations of disordered superconduct ors in which the quasiparticle spin is not conserved. We analyze one-dimens ional models with this RG and with elementary transfer matrix methods. We f ind that such models with broken spin rotation invariance generically lie i n one of two topologically distinct localized phases. Close enough to the c ritical point separating the two phases, the system has a power-law diverge nt low-energy density of states (with a nonuniversal continuously varying p ower law) in either phase, due to quantum Griffiths singularities. This cri tical point belongs to the same infinite-disorder universality class as the one-dimensional particle-hole symmetric Anderson localization problem, whi le the Griffiths phases in the vicinity of the transition are controlled by lines of strong (but not infinite) disorder fixed points terminating in th e critical point.