the numerical methods employed for this study, namely Variational Monte Carlo (VMC) and DMC. Results obtained for both the spin-balanced and spin-imbalanced cases are then presented in Section \[sec:results\], followed by a discussion on the effects of changing various simulation parameters. Conclusions are presented in Section \[sec:conclusion\].

Quantum Monte Carlo
===================

We use the <span style="font-variant:small-caps;">casino</span> code [@casino] to perform our quantum Monte Carlo study of the Hamiltonian $$\begin{aligned}
H = \sum_{i}\frac{\nabla^{2}_{i}}{2}+\sum_{i,j}V({\mathbf{r}}_i-{\mathbf{r}}_j)\end{aligned}$$ where $i$ and $j$ index the fermions, ${\mathbf{r}}_i$ is the position vector of fermion $i$, and $V$ is the interaction potential. The fermions are of equal mass and we work in a combination of natural and Hartree units so $\hbar=c=e=m=1$.

Pseudopotential {#sec:pseudopot}
---------------

We use an ultratransferable pseudopotential (UTP) [@2dscapseudopot], a continuous, differentiable, piecewise defined polynomial that can be optimized to match the scattering phase shift of a known target potential over a range of incident momenta. The UTP is defined such that it is nonzero for distances less than a cutoff length ${L_\mathrm{c}}$ and zero beyond. ${L_\mathrm{c}}$ thus controls the extent of the potential in real space and in App. \[subsec:simparams\] is chosen to be equal to ${r_\mathrm{s}}$, the average interparticle separation and the typical length scale 