Emergent BCS regime of the two-dimensional fermionic Hubbard model:   ground-state phase diagram
  A significant part of the phase diagram of the two-dimensional fermionic Hubbard model for moderate interactions and filling factors ($U < 4, \, n<0.7$) is governed by effective Fermi liquid physics with weak BCS-type instabilities. We access this regime in a controlled way by a combination of the bold-line diagrammatic Monte Carlo method with an additional ladder-diagram summation trick and semi-analytic treatment of the weak instability in the Cooper channel. We obtain the corresponding ground-state phase diagram in the $(n,U)$ plane describing the competition between the $p-$ and $d-$wave superfluid states. We also claim the values of the dimensionless BCS coupling constants controlling the superfluid $T_c$ at the phase boundaries, which prove to be very small up to $U=4, n = 0.6$. 
Youjin Deng, Evgeny Kozik, Nikolay V. Prokof'ev, Boris V. Svistunov
cond-mat.str-el cond-mat.stat-mech physics.comp-ph