# Majorana Quasi-Particles Protected by $\mathbb{Z}_2$ Angular Momentum Conservation

## TL;DR

This paper demonstrates how angular momentum conservation can stabilize Majorana quasi-particles in a one-dimensional cold atom system, offering a robust, reservoir-independent protection mechanism.

## Contribution

It introduces a number-conserving Hubbard model with spin-orbit coupling that supports Majorana edge modes protected by angular momentum parity symmetry.

## Key findings

- Majorana modes emerge in the model with spin-orbit coupling.
- Density-matrix-renormalization-group confirms the edge states.
- The mechanism is robust without reservoir coupling.

## Abstract

We show how angular momentum conservation can stabilise a symmetry-protected quasi-topological phase of matter supporting Majorana quasi-particles as edge modes in one-dimensional cold atom gases. We investigate a number-conserving four-species Hubbard model in the presence of spin-orbit coupling. The latter reduces the global spin symmetry to an angular momentum parity symmetry, which provides an extremely robust protection mechanism that does not rely on any coupling to additional reservoirs. The emergence of Majorana edge modes is elucidated using field theory techniques, and corroborated by density-matrix-renormalization-group simulations. Our results pave the way toward the observation of Majorana edge modes with alkaline-earth-like fermions in optical lattices, where all basic ingredients for our recipe - spin-orbit coupling and strong inter-orbital interactions - have been experimentally realized over the last two years.