Fig. 2.

QMC results on the triangular lattice with size $L\times L$, where the EPC strength is fixed at $\lambda =2.16$ (corresponding to $g=1.8$). (A) The correlation-length ratio (defined in Eq. 2) for onsite s-wave superconducting order as a function of ${\omega }_0$. The crossing point for different system sizes indicates that the transition between the SC and non-SC (QSL) phases occurs at ${\omega }_0\approx 1.2$. (B) The Binder ratio (defined in SI Appendix, Eq. S5) for SVBS order as a function of ${\omega }_0$. The transition between SVBS and the uniform (QSL) phase occurs at ${\omega }_0\approx 0.7$. (C) Finite-size-scaling results of the single-particle and spin gaps, ${\mathrm{\Delta }}_{\mathrm{single}}$ and ${\mathrm{\Delta }}_{\mathrm{spin}}$, in the QSL phase for ${\omega }_0=1.0$. Both ${\mathrm{\Delta }}_{\mathrm{single}}$ and ${\mathrm{\Delta }}_{\mathrm{spin}}$ extrapolate to finite values as $L\to \infty$, confirming the fully gapped character of the QSL phase.