# Response functions for the two-dimensional ultracold Fermi gas: dynamical BCS theory and beyond

## TL;DR

This paper investigates response functions in a 2D ultracold Fermi gas using dynamical BCS theory and auxiliary-field quantum Monte Carlo, providing insights into their accuracy and applicability across interaction regimes.

## Contribution

It applies dynamical BCS theory to 2D ultracold Fermi gases and compares results with AFQMC methods to evaluate their accuracy.

## Key findings

- Dynamical BCS theory effectively describes response functions in certain regimes.
- AFQMC provides benchmark results for imaginary-time correlations.
- Comparisons reveal the strengths and limitations of dynamical BCS in 2D Fermi gases.

## Abstract

Response functions are central objects in physics. They provide crucial information about the behavior of physical systems, and they can be directly compared with scattering experiments involving particles like neutrons, or photons. Calculations of such functions starting from the many-body Hamiltonian of a physical system are challenging, and extremely valuable. In this paper we focus on the two-dimensional (2D) ultracold Fermi atomic gas which has been realized experimentally. We present an application of the dynamical BCS theory to obtain response functions for different regimes of interaction strengths in the 2D gas with zero-range attractive interaction. We also discuss auxiliary-field quantum Monte Carlo (AFQMC) methods for the calculation of imaginary-time correlations in these dilute Fermi gas systems. Illustrative results are given and comparisons are made between AFQMC and dynamical BCS theory results to assess the accuracy of the latter.