communal, but has the appropriate values of $({N_\uparrow},{N_\downarrow})=(2,1)$.

Similar results were obtained on performing exact diagonalisation at the Fermi surface of the system with 25 and 9 fermions on the square lattice; FFLO theory predicts a 4-fold degenerate peak at $q^{}_{\mathrm{FFLO}}=\sqrt{2}G$ and zero condensate fraction otherwise while the communal exact diagonalisation results for $({N_\uparrow},{N_\downarrow})=(2,1)$ and $(3,1)$ exhibited nonzero condensate over a range of momenta with a global maximum at $q^{}_{\mathrm{FFLO}}$. The test statistic obtained repeats the conclusion that the system is best described by a communal state with $({N_\uparrow},{N_\downarrow})=(2,1)$.

The mismatch between the DMC and communal exact diagonalisation results, particularly at $q=0$, may be due to a number of factors. Firstly, exact diagonalisation only accounts for a subset of the allowed momentum states without considering states above the Fermi surfaces, and secondly, that exact diagonalisation was carried out for only 2 (FFLO), 3 or 4 (communal) particles in total.

[0.85]{} ![Condensate fraction in momentum space for different ratios of majority to minority species fermions at the Fermi surfaces. 37 majority and 7 minority fermions create a 3:1 spin imbalance at the Fermi surfaces and 61 majority and 7 minority fermions create a 4:1 spin imbalance.[]{data-label="imbas"}](3_1sy "fig:"){width="\linewidth"}

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[0.85]{} ![Condensate fraction 