Majorana modes meet fractional fermions in one dimension

TL;DR

This paper demonstrates how to realize and analyze a one-dimensional chain that hosts both Majorana modes and fractional fermions simultaneously, revealing their spin-charge separation and symmetry protection.

Contribution

It introduces a novel lattice model combining Majorana modes and fractional fermions, and explores their properties using multiple theoretical methods.

Findings

Edge modes are protected by inversion and spin-parity symmetries.

The model exhibits four-fold degenerate ground states with edge-spinons.

Haldane phase ground states can be reinterpreted as spin-charge separated edge modes.

Abstract

Majorana modes and fractional fermions are two types of edge zero modes appearing separately in topological superconductors and dimerized chains. Here we reveal how to harvest both types of edge modes simultaneously in an exotic chain. Such modes are naturally spin-charge separated, and are protected by the inversion and spin-parity symmetries. We construct a lattice model to illustrate the nature of these edge modes, utilizing fermionic functional renormalization group, mean-field theory and bosonization. We also elucidate that the four-fold degenerate ground states with edge-spinons in the Haldane phase of spin-$1$ chain may be reinterpreted as our spin-charge separated edge modes in an equivalent spin-$1/2$ fermionic model.