# Majorana edge modes in number-conserving models with long-range interactions

## TL;DR

This paper numerically investigates number-conserving long-range interacting models, providing evidence for Majorana edge modes in finite systems without mean-field assumptions, and introduces a correlation-based method to analyze their structure.

## Contribution

It demonstrates the existence of Majorana edge modes in number-conserving, long-range interacting models and develops a new correlation-based approach to study their spatial structure.

## Key findings

- Majorana edge modes appear in open chains with long-range interactions.
- Energy splitting between parity sectors vanishes with increasing system size.
- Nonlocal, parity-dependent edge correlations are observed.

## Abstract

Topological superconductors are believed to host exotic quasiparticle excitations known as Majorana zero-modes, with much of the evidence based on BCS mean-field theory. The direct application of mean-field arguments is tenuous in finite, isolated systems relevant in some experiments. Here, we numerically study fermion number-conserving models with long-range interactions, which under periodic boundary conditions exhibit robust topological and non-topological superconductivity, tuned by the strength of interaction [1]. We find evidence that, on the topological side, Majorana edge modes appear in open chains, manifesting as the vanishing of the energy splitting between odd- and even-parity ground states with increasing system size. Additionally, off-diagonal two-point correlation functions show nonlocal, parity-dependent edge effects consistent with Majorana phenomenology. We develop a correlation-based method revealing the spatial structure of Majorana modes in this fully interacting many-body setting.