Diagrammatic Monte-Carlo approach to many-flavour unitary fermions

The difficulty of understanding strongly correlated matter is often related to the absence of a natural small parameter providing a starting point for a perturbative treatment. Large-$N$ approaches provide a prominent theoretical tool, which seeks to address this issue for fermionic theories by introducing a generalised theory with many fermion flavours, that then becomes amenable to perturbative treatments.

We demonstrate how to implement this concept in conjunction with a diagrammatic Monte-Carlo approach, using a many fermion-flavour generalisation of the unitary Fermi gas [1] for illustration. This system provides an ideal test case thanks to existing diagrammatic Monte-Carlo techniques developed in [2,3], which yield a numerically exact solution thanks to explicit resummation of the high-order asymptotics [4].
We present results on the extended large-$N$ generalisation of the theory [5,6], and demonstrate how to apply diagMC in this setting. Using the resummation technique developed by Rossi et al [4], we show that the convergence radius in the Borel plane is enlarged as a function of fermion flavours, thus facilitating the convergence of the series in the vicinity of the transition into the superfluid phase.
We argue that the combination of large-$N$ field theory techniques with high-order numerical resummations opens up a new avenue for investigations of strongly interacting systems more generally.

[1] W. Zwerger, Springer (2012).
[2] K. v.Houcke et al., Nat Phys 8, 366 (2012).
[3] K. v.Houcke et al., PRB 99, 035140 (2019).
[4] R. Rossi, et al., PRL 121, 130405 (2018).
[5] M.Y. Veillette, et al., PRA 75, 043614 (2007).
[6] P. Nikolic and S. Sachdev, PRA 75, 033608 (2007).