# Many-Body Entanglement in Short-Range Interacting Fermi Gases for Metrology

## TL;DR

This paper investigates many-body entanglement in short-range interacting Fermi gases, demonstrating how quantum Fisher information can serve as an order parameter to identify metrologically useful entanglement in novel quantum phases.

## Contribution

It introduces a method to use quantum Fisher information as an order parameter for entanglement in Fermi gases, highlighting the role of short-range interactions in generating metrologically valuable entanglement.

## Key findings

- Short-range interactions induce entanglement in XY-ferromagnetic phases.
- Quantum Fisher Information effectively characterizes quantum phases.
- Cluster ordering physics is identified as a new avenue for entanglement studies.

## Abstract

We explore many-body entanglement in spinful Fermi gases with short-range interactions, for metrology purposes. We characterize the emerging quantum phases via Density-Matrix Renormalization Group simulations and quantify their entanglement content for metrological usability via the Quantum Fisher Information (QFI). Our study establishes a method, promoting the QFI to be an order parameter. Short-range interactions reveal to build up metrologically promising entanglement in the XY-ferromagnetic and cluster ordering, the cluster physics being unexplored so far.