Response Functions for the Two-Dimensional Ultracold Fermi Gas: Dynamical BCS Theory and Beyond

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.

Variational and Parquet-diagram theory for strongly correlated normal and superfluid systems

“…There have been several suggestions for a Lindhard function for a superfluid system [118,18,19,21], the most frequently used form for T = 0 is given below. In view of the need for the spin-spin response function in Section 6.1 we cite here both the spin and the density channels.…”

“…Rather, we shall focus on the technical aspects of many-body theory and spend very little space reviewing and comparing specific calculations. A theory for superfluid many-body systems of the same diagrammatic completeness that was achieved for normal systems is presently unavailable, although specific partial summations of the perturbation series have been carried out [18,19,20,21]. A version of Coupled Cluster theory for BCS-type wave functions has also been developed [22].…”

Dynamical BCS Theory of a Two-Dimensional Attractive Fermi Gas: Effective Interactions from Quantum Monte Carlo Calculations

“…This is equivalent to constraining the system to move on the above mentioned lattice. The original Hamiltonian can be recovered by performing the continuum limit b → 0 together with the thermodynamic limit L → +∞ [14]. The regularized Hamiltonian in momentum space is the Hubbard Hamiltonian for cold atoms, with a modified dispersion relation proportional to |k| 2 , consistent with the continuum limit and the diluteness condition, the average number of particles being always much smaller than the number of lattice sites.…”

“…Building on a recent study [14], we start our investigation at high momentum, |q| 4k F . This regime is important, since the dynamical structure factor is a very interesting probe to distinguish between the individual particles and the molecules.…”

“…Normally this is achieved by mean field approaches and the difficulty lies in the fact that, in general, the underlying approximations are uncontrollable and it is difficult to draw robust physical conclusions. This is exactly the motivation for our study: in this work we will build on our previous study [14], where we made a simple comparison between AFQMC and the state-of-art dynamical BCS theory [15]. We explore whether it is possible to use the exact AFQMC results in imaginary time as an asset to assess and improve the dynamical BCS predictions through a suitable renormalization of the parameters.…”