We study spin transport in a Hubbard chain with strong, random, on-site potential and with spin-dependent hopping integrals, tσ. For the the SU(2) symmetric case, t ↑ = t ↓ , such model exhibits only partial many-body localization with localized charge and (delocalized) subdiffusive spin excitations. Here, we demonstrate that breaking the SU(2) symmetry by even weak spinasymmetry, t ↑ = t ↓ , localizes spins and restores full many-body localization. To this end we derive an effective spin model, where the spin subdiffusion is shown to be destroyed by arbitrarily weak t ↑ = t ↓ . Instability of the spin subdiffusion originates from an interplay between random effective fields and singularly distributed random exchange interactions.

We study a quantum particle coupled to hard-core bosons and propagating on disordered ladders with R legs. The particle dynamics is studied with the help of rate equations for the boson-assisted transitions between the Anderson states. We demonstrate that for finite R < ∞ and sufficiently strong disorder the dynamics is subdiffusive, while the two-dimensional planar systems with R → ∞ appear to be diffusive for arbitrarily strong disorder. The transition from diffusive to subdiffusive regimes may be identified via statistical fluctuations of resistivity. The corresponding distribution function in the diffusive regime has fat tails which decrease with the system size L much slower than 1/ √ L. Finally, we present evidence that similar non-Gaussian fluctuations arise also in standard models of many-body localization, i.e., in strongly disordered quantum spin chains.

Topological phases of matter are among the most intriguing research directions in Condensed Matter Physics. It is known that superconductivity induced on a topological insulator’s surface can lead to exotic Majorana modes, the main ingredient of many proposed quantum computation schemes. In this context, the iron-based high critical temperature superconductors are a promising platform to host such an exotic phenomenon in real condensed-matter compounds. The Coulomb interaction is commonly believed to be vital for the magnetic and superconducting properties of these systems. This work bridges these two perspectives and shows that the Coulomb interaction can also drive a canonical superconductor with orbital degrees of freedom into the topological state. Namely, we show that above a critical value of the Hubbard interaction the system simultaneously develops spiral spin order, a highly unusual triplet amplitude in superconductivity, and, remarkably, Majorana fermions at the edges of the system.