Many-body Majorana operators and the equivalence of parity sectors

Abstract

The one-dimensional p-wave topological superconductor model with open-boundary conditions is examined in its topological phase. Using the eigenbasis of the non-interacting system I show that, provided the interactions are local and do not result in a closing of the gap, then even and odd parity sectors are unitarily equivalent. Following on from this, it is possible to define two many-body operators that connect each state in one sector with a degenerate counterpart in the sector with opposite parity. This result applies to all states in the system and therefore establishes, for a long enough wire, that all even-odd eigenpairs remain essentially degenerate in the presence of local interactions. Building on this observation I then set out a full definition of the related many-body Majorana operators and point out that their structure cannot be fully revealed using cross-correlation data obtained from the ground state manifold alone. Although all results are formulated in the context of the 1-dimensional p-wave model, I argue why they should also apply to more realistic realisations (e.g. the multi-channel p-wave wire and proximity coupled models) of topological superconductivity.

8 pages, 1 figure

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• Parafermionic phases with symmetry-breaking and topological order
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• Parafermionic clock models and quantum resonance
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• Almost Strong Zero Modes at Finite Temperature
• Critical region of topological trivial and nontrivial phases in interacting Kitaev chain with spatially varying potentials
• Dynamical Phase Error in Interacting Topological Quantum Memories
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• Density matrix renormalization group study of the interacting Kitaev chain with quasi-periodic disorder
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• Floquet Gauge Pumps as Sensors for Spectral Degeneracies Protected by Symmetry or Topology
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