Unitary Electron Gas Problem

In quantum emulation, the focus has largely been on short-range interactions. However, when considering fermions, particularly electrons, in real-world scenarios, one cannot overlook the significant role of long-range Coulomb interactions. This research extends the conventional unitary Fermi gas model, characterized by local contact attraction, by integrating the challenges posed by charged fermions and their accompanying long-range Coulomb repulsion. The resulting phase diagram combines BEC-BCS crossover phenomena with uniform electron gas properties, offering a more comprehensive view of fermionic interactions. This model serves as a vital bridge, linking the controlled environments of ultracold atom emulators to the intricacies of electron liquid systems in real materials. To decode the uniform electron problem, we've developed a novel electron liquid field theory encompassing dynamically screened Coulomb interactions and local attractions. The systematic solution of this field theory is made possible through our "Numerical Effective Field Theory" toolbox. The findings from this research hold relevance for both ultracold atom and material science disciplines.