# Ising anyonic topological phase of interacting Fermions in one dimension

## TL;DR

This paper investigates a one-dimensional interacting fermion system that exhibits an Ising anyonic topological phase, analyzing its stability and the symmetry requirements for its protection through theoretical and numerical methods.

## Contribution

It identifies the conditions under which the Ising anyonic topological phase persists in an interacting fermion ladder model, highlighting the role of symmetry in its stability.

## Key findings

- Topological phase survives over an extended parameter regime.
- An additional symmetry is necessary to protect the topological phase.
- The phase diagram is mapped using bosonization and DMRG techniques.

## Abstract

We study a microscopic model of interacting fermions in a ladder setup, where the total number of particles is conserved. At a special point, the ground state is known and gives rise to a topological state of matter with edge modes obeying the statistics of Ising anyons. Using a combination of bosonization as well as full scale numerical density-matrix renormalization group analysis, we map out the full phase diagram. We nd that the topological phase survives in an extended parameter regime. Remarkably, an additional symmetry is required to protect the topological phase.