# Ground State Energy of Dilute Fermi Gases in 1D

## TL;DR

This paper analyzes the ground state energy of a dilute spin-J Fermi gas with repulsive interactions in one dimension, linking it to the energy of a related spin chain model.

## Contribution

It establishes the asymptotic behavior of the ground state energy for the dilute Fermi gas in 1D, connecting it to the Heisenberg antiferromagnet for spin-1/2.

## Key findings

- Derived asymptotics of the ground state energy in the dilute limit.
- Linked the Fermi gas energy to the energy of a spin chain model.
- Provided a rigorous mathematical framework for the asymptotic analysis.

## Abstract

We study the spin-J Fermi gas, interacting through a general repulsive 2-body potential, and prove asymptotics of the ground state energy in the dilute limit. The asymptotic behaviour is given in terms of the ground state energy of a spin chain, which is the Heisenberg antiferromagnet in the case of spin-1/2 fermions.