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

TL;DR

This paper maps the superfluid ground-state phase diagram of the 2D Hubbard model using a diagrammatic Monte Carlo approach, revealing complex doping-dependent phases and connections to high-temperature superconductivity.

Contribution

It introduces a controlled Monte Carlo method to compute effective couplings and systematically explores the phase diagram across various parameters.

Findings

Phase diagram is highly sensitive to doping and next-nearest-neighbor hopping.

At high doping and $t'$, a transition from triplet to singlet pairing occurs.

Results are consistent with $d_{x^2-y^2}$ superconductivity near cuprates' optimal doping.

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 $0 \leq t^{\prime} \leq 0.3t$, interaction strength $0 \leq U \leq 3t$, and lattice filling $0 \leq n \leq 2$. 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 $n \approx 0.73$ 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.