# Lieb-Robinson bounds, the spectral flow, and stability of the spectral gap for lattice fermion systems

## TL;DR

This paper establishes Lieb-Robinson bounds for lattice fermion systems, enabling analysis of spectral flow and stability of spectral gaps, which are crucial for understanding quantum phases and topological order.

## Contribution

It extends Lieb-Robinson bounds and spectral flow techniques from spin systems to fermionic lattice models, demonstrating spectral gap stability under certain conditions.

## Key findings

- Lieb-Robinson bounds proven for fermion systems
- Spectral flow automorphisms constructed for these systems
- Spectral gap stability shown for frustration-free models

## Abstract

We prove Lieb-Robinson bounds for a general class of lattice fermion systems. By making use of a suitable conditional expectation onto subalgebras of the CAR algebra, we can apply the Lieb-Robinson bounds much in the same way as for quantum spin systems. We preview how to obtain the spectral flow automorphisms and to prove stability of the spectral gap for frustration-free gapped systems satisfying a Local Topological Quantum Order condition.