made it possible to simulate many-body quantum systems, affording us a fresh avenue of investigation into the pairing structure of these exotic systems. In the present study we focus exclusively on two-dimensional systems as low dimensionality is thought to enhance the stability of FFLO-like phases [@fflostability1; @fflostability2; @fflostability3] and is the lowest dimension in which states different from FFLO but with space varying gap parameter are predicted [@multipartsupconfew].

Diffusion Monte Carlo (DMC) simulations offer a fast method to study spin-imbalanced fermion gases [@riospairingorb; @dmcfermion1; @dmcfermion2]. It is exact except for a fixed node approximation and so includes all orders of correlators and loop diagrams. Furthermore, the temperature of the system can be kept constant, even at absolute zero, and so the fermion spins can be prevented from relaxing. Using this technique, we investigate fermion pairing at nonzero pair momenta, demonstrating a spatially non-uniform superconductor. Furthermore, the distribution of the condensate fraction in momentum space is similar to that predicted by communal pairing theory [@commupair] and markedly different to that predicted by FFLO theory. This provides evidence that non-exclusive pairing is the ground state of the spin-imbalanced superconductor.

In the next section we introduce the Hamiltonian for the problem and summarise 