The superconducting pairing symmetry is significantly constrained by lattice symmetry, yet how this pairing symmetry evolves with changes in lattice symmetry remains unclear. In this study, through variational quantum Monte Carlo simulations on the Hubbard model, we investigate the evolution of the superconducting ground state on an anisotropic triangular lattice with smoothly tunable frustration. At half-filling, we identify a hidden
C6-like
s+d+id-wave superconductivity, which breaks time-reversal symmetry, emerging for moderate frustrations. This occurs as the lattice symmetry transitions from
C4 to
C2, where the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave and
s+dxy-wave superconducting ground states dominate, respectively. Notably, we find an isotropic-like
d+id-wave superconducting phase at ${t}^{\ensuremath{'}}/t\ensuremath{\approx}0.7$, much lower than the expected value ${t}^{\ensuremath{'}}/t=1$ predicted by most previous studies. At high electron doping levels, we further discover an unexpected quasi-one-dimensional ${d}_{xy}^{\ensuremath{'}}$-wave superconductivity characterized by strong pairing on the next-nearest-neighbor bond, despite the absence of direct hopping. The numerical data also reveal that pairing symmetries, belonging to distinct irreducible representations of the given point group, can mix together, beyond the conventional theories based on the linear gap equations.
Spin-triplet superconductivity is actively pursued in condensed matter physics due to the potential applications in topological quantum computations. The related pairing mechanism involving the interaction remains an important research topic. Here we propose a universal approach to obtain p-wave triplet superconductivity in the Hubbard models by simply changing the sign of the hopping amplitudes of the spin-down electrons, and apply it to three prototype two-dimensional lattices (honeycomb, square, and triangular). The parent Hamiltonian at half filling has long-range magnetic order, which is ferromagnetic in all three directions for the frustrated triangular lattices, and ferromagnetic (antiferromagnetic) in the xy plane (z direction) for the bipartite honeycomb and square lattices. The magnetic transitions occur at some critical interactions on honeycomb and triangular lattices, which are estimated by finite-size scalings. When the systems are doped, we find the triplet p-wave pairing is a dominating superconducting instability. We demonstrate its emergence is closely related to the strong ferromagnetic spin fluctuations induced by the doping. Our results provide an understanding of the microscopical triplet-pairing mechanism, and will be helpful in the search for spin-triplet superconducting materials.