Superfluid ground state phase diagram of the two-dimensional Hubbard model in the emergent Bardeen-Cooper-Schrieffer regime

Abstract

In nonperturbative regimes, the superfluid instability in the two-dimensional Hubbard model can be described by an emergent BCS theory with small effective pairing constants. We compute the effective couplings using a controlled bold-line diagrammatic Monte Carlo approach, which stochastically sums all skeleton Feynman diagrams dressed in the one- and two-particle channels to high expansion orders, and map out the resulting superfluid ground-state phase diagram in a range of next-nearest-neighbor hopping $0\le t^{\prime }\le 0.3t$, interaction strength $0\le U\le 3t$, and lattice filling $0\le n\le 2$. The phase diagram is dramatically transformed in the hole-doped region and becomes particularly rich at larger doping and $t^{\prime }$. At $t^{\prime }=0.3$, the weak-coupling picture with the dominant triplet pairing sharply peaked at $n\approx 0.73$ due to the Van Hove singularity is replaced by a plateau of the singlet $d_{x^2-y^2}$ paring, while for $U\gtrsim 3t$ the effective couplings are consistent with the $d_{x^2-y^2}$ high-temperature superconductivity in the hole-doped region near cuprates' optimal doping.

6 pages, 4 figures