Exact weak bosonic zero modes in a spin/fermion chain

TL;DR

This paper investigates an exactly solvable 1D spin chain model that supports weak zero modes, which are bosonic and can be realized experimentally, by analyzing its phase diagram and zero mode properties.

Contribution

It introduces a new exactly solvable spin chain model with weak zero modes and characterizes their properties and conditions for existence.

Findings

Weak zero modes are bosonic and polynomial in Majorana operators.

The model's phase diagram is mapped out.

Potential experimental realization of the fermionic chain is discussed.

Abstract

We study an exactly solvable one-dimensional spin-$\frac{1}{2}$ model which can support weak zero modes in its ground state manifold. The spin chain has staggered XXZ-type and ZZ-type spin interaction on neighboring bonds and is thus dubbed the (XXZ,Z) chain. The model is equivalent to an interacting fermionic chain by Jordan-Wigner transformation. We study the phase diagram of the system and work out the conditions and properties of its weak zero modes. In the fermion chain representation, these weak zero modes are given by even-order polynomials of Majorana fermion operators and are thus bosonic. The fermionic chain Hamiltonian contains only fermion hopping and interaction terms and may have potential realization in experiments.