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

In nonperturbative regimes, the superfluid instability in the two-dimensional (2D) 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 <= t' <= 0.3t, interaction strength 0 <= U <= 3t, and lattice filling 0 <= n <= 2. The phase diagram is dramatically transformed in the hole-doped region and becomes particularly rich at larger doping and t'. At t' = 0.3, the weak-coupling picture with the dominant triplet pairing sharply peaked at n approximate to 0.73 due to the Van Hove singularity is replaced by a plateau of the singlet d(x2-y2) paring, while for U greater than or similar to 3t the effective couplings are consistent with the d(x2-y2) high-temperature superconductivity in the hole-doped region near cuprates' optimal doping.

Automated summary

This study investigates the superfluid instability in the 2D Hubbard model using a nonperturbative approach and maps out the superfluid ground-state phase diagram under various parameter ranges. The phase diagram undergoes dramatic transformations in different regions, showing rich physical phenomena under different parameter conditions.