Abstract

We investigate a majorana chain model with potential applications to the description of Kitaev edges. The model exhibits various topological phases which are separated by critical lines. Since the non-interacting system belongs to class BDI one would expect these lines to remain critical in presence of disorder if the interaction is sufficiently weak.
Recent numerical studies using DMRG confirm this for attractive interactions. For strong repulsive interactions, these studies find that the system localizes.
Our results show localization also for weak repulsive interaction. We want to understand the mechanism that drives the system into localization despite topological protection.
To reach this goal we employ both DMRG calculations and diverse analytical RG-schemes.
DMRG suggests spontaneous breaking of the translation symmetry.
This cannot be understood from the weak disorder and weak interaction RG around the clean noninteracting fixed point (FP), where the interaction is irrelevant. Hence we investigate the stability of the infinite randomness FP against weak interaction.
The wave functions exhibit (multi)fractality. Correlators are again computed analytically using a SUSY transfer matrix techniques. This approach is augmented by results from exact diagonalization. From their scaling behaviour we deduce the interaction RG flow.

References:
PRB 92, 235123
PRL 109, 246801
PRB 56, 12970