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

TL;DR

This paper constructs a strong zero mode in the XYZ chain with interactions, revealing eigenstate phase transitions and spectral pairing, extending understanding of symmetry and localization in quantum many-body systems.

Contribution

It explicitly constructs a strong zero mode in an interacting XYZ chain, demonstrating spectral pairing and eigenstate phase transitions in a clean, interacting system.

Findings

Strong zero mode pairs states across symmetry sectors.

Eigenstate phase transitions separate different pairing regimes.

Zero mode squares to identity, showing a remarkable structure.

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.