Uncovering Exotic Paired States in the 2D Spin-Imbalanced Fermi Gas with Neural Wave Functions

We study the zero-temperature phase diagram of the 2D spin-imbalanced Fermi gas with short-ranged attractive interactions using the recently developed neural network variational Monte Carlo method with the AGPs FermiNet Ansatz. The Fulde-Ferrell-Larkin-Ovchinnikov phase is observed in the weakly interacting BCS limit and a polarised superfluid is seen in the strongly interacting BEC limit. When the interactions are strong, the minority-spin momentum density is reduced almost to zero in the momentum-space region occupied by the unpaired majority-spin electrons. When the interactions are very strong, phase separation occurs, with regions containing bosonic pairs and unpaired regions occupied by the remaining majority-spin particles. In addition, we observe translational symmetry breaking at intermediate interaction strengths, where the system forms an exotic crystal of Cooper pairs in a Fermi fluid of unpaired majority-spin particles. We provide a possible explanation for the formation of the crystalline phase, explain the origins of the k-space momentum-density hole when the pairs are tightly bound, and discuss how our approach opens new directions for future work.