High-order expansion around BCS theory

In contrast to conventional QMC methods, expansions of intensive quantities in series of connected Feynman diagrams can be formulated directly in the thermodynamic limit. Over the last decade, new Monte Carlo algorithms made it possible to reach large expansion orders and to obtain accurate results for various key models of interacting fermions in previously inaccessible regimes.

We report first results inside the superfluid phase of the attractive Hubbard model. Expanding around the BCS Hamiltonian, we sum up all diagrams up to order ~12 thanks to the connected determinant algorithm [1]. Working on the BCS side of the strongly correlated regime, we observe convergence of the expansion. We benchmark our results against determinant diagrammatic Monte Carlo [2] in the unpolarized regime. In the polarized regime, we accurately locate the first-order superfluid-to-normal phase transition. We also find that the expansion has a non-exponential large-order behavior associated to peculiar singularities as a function of the formal expansion parameter xi, one of them coming from the Goldstone mode and another one from a first order transition as a function of xi.

[1] R. Rossi, PRL 119, 045701 (2017).
[2] E. Burovski et al., PRL 96, 160402 (2006).