# Fermions in Two Dimensions: Scattering and Many-Body Properties

## TL;DR

This paper investigates the properties of two-dimensional ultracold Fermi gases across different interaction regimes using ab initio Monte Carlo methods, focusing on scattering theory and many-body ground-state characteristics.

## Contribution

It provides a detailed analysis of 2D scattering parameters and computes ground-state properties of strongly interacting Fermi gases with variational wave functions.

## Key findings

- Calculated scattering length and effective range in 2D.
- Determined ground-state energy and equation of state.
- Analyzed chemical potential in strongly interacting regime.

## Abstract

Ultracold atomic Fermi gases in two-dimensions (2D) are an increasingly popular topic of research. The interaction strength between spin-up and spin-down particles in two-component Fermi gases can be tuned in experiments, allowing for a strongly interacting regime where the gas properties are yet to be fully understood. We have probed this regime for 2D Fermi gases by performing T=0 ab initio diffusion Monte Carlo calculations. The many-body dynamics are largely dependent on the two-body interactions, therefore we start with an in-depth look at scattering theory in 2D. We show the partial-wave expansion and its relation to the scattering length and effective range. Then we discuss our numerical methods for determining these scattering parameters. We close out this discussion by illustrating the details of bound states in 2D. Transitioning to the many-body system, we use variationally optimized wave functions to calculate ground-state properties of the gas over a range of interaction strengths. We show results for the energy per particle and parametrize an equation of state. We then proceed to determine the chemical potential for the strongly interacting gas.