Unwinding of a one-dimensional topological superconductor

Abstract

We show that a topological superconductor made of four chains of superconducting spinless fermions characterized by four Majorana edge states can adiabatically be deformed into a trivial band insulator. To unwind this time-reversal invariant topological superconductor, interactions to spinful fermions are switched on along an adiabatic path. Thereby, we couple modes which belong to two different representations of the time-reversal symmetry operator $\mathcal{T}$ with ${\mathcal{T}}^{2}=1$ and ${\mathcal{T}}^{2}=\ensuremath{-}1$, respectively. This observation can be understood by investigating how the relevant symmetries act on the entanglement spectrum giving rise to four instead of eight different topological phases with Majorana edge modes. We also show that a simple level crossing of doubly and singly degenerate states occurs in the entanglement spectrum on deforming the quantum state.