We explore a new avenue for quantitative investigations of strongly interacting systems by combining large-N fermionic theories with a stochastic sampling of high order Feynman graphs.

Our work focuses on the unitary Fermi gas as a blueprint example for a strongly interacting system of fermions without a small expansion parameter in the Hamiltonian [1]. Seminal work on this problem has established a diagrammatic Monte-Carlo (diagMC) approach [2], which has recently been completed by exploring the high order asymptotic of the series expansion [3]. Here, we re-examine the problem by introducing a small parameter via a large-N generalization with multiple fermion flavors [4,5], to which we then apply diagMC. Formally, this yields an expansion around the mean-field superconducting theory, whose properties are recovered in the $N\to\infty$ limit.

Our proposal opens up a new avenue for investigations of strongly interacting systems by promoting large-N theories to a more quantitative tool suitable for accurate numerical studies at high orders in the inverse number of flavors.

[1] W. Zwerger, Springer (2012).

[2] Van Houcke, K. et al., Nat Phys 8, 366 (2012); and Van Houcke, K., Werner F., Prokof’ev, N. & Svistunov, B., arXiv:1305.3901 (2013).

[3] Rossi, R., Ohgoe, T., Van Houcke, K. & Werner, F., arXiv:1802.07717 (2018).

[4] Veillette, M. Y., Sheehy, D. E. & Radzihovsky, L. Phys. Rev. A 75, 043614 (2007).

[5] Nikolic, P. & Sachdev, S. Phys. Rev. A 75, 033608 (2007).