Strong zero modes and eigenstate phase transitions in the XYZ/interacting Majorana chain

Abstract

I explicitly construct a strong zero mode in the XYZ chain or, equivalently, Majorana wires coupled via a four-fermion interaction. The strong zero mode is an operator that pairs states in different symmetry sectors, resulting in identical spectra up to exponentially small finite-size corrections. Such pairing occurs in the Ising/Majorana fermion chain and possibly in parafermionic systems and strongly disordered many-body localized phases. The proof here shows that the strong zero mode occurs in a clean interacting system, and that it possesses some remarkable structure -- despite being a rather elaborate operator, it squares to the identity. Eigenstate phase transitions separate regions with different types of pairing.

5 pages plus a 6-page appendix containing a proof

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