Unwinding of a one-dimensional topological superconductor

TL;DR

This paper demonstrates how a one-dimensional topological superconductor with Majorana edge states can be smoothly transformed into a trivial insulator by introducing interactions, revealing new insights into topological phase transitions and symmetry effects.

Contribution

It introduces an adiabatic deformation pathway that unwinds a topological superconductor into a trivial insulator by coupling to spinful fermions and analyzing symmetry actions on the entanglement spectrum.

Findings

Topological superconductor can be deformed into a trivial insulator without closing the bulk gap.

Interactions change the classification from eight to four topological phases.

Entanglement spectrum shows level crossings indicating phase transitions.

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 T with T^2 = 1 and T^2 = -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 upon deforming the quantum state.