High Temperature Superconductivity in a Lightly Doped Quantum Spin Liquid

We have performed density-matrix renormalization group studies of a square lattice $t\text{\ensuremath{-}}J$ model with small hole doping, $\ensuremath{\delta}\ensuremath{\ll}1$, on long four and six-leg cylinders. We include frustration in the form of a second-neighbor exchange coupling, ${J}_{2}={J}_{1}/2$, such that the undoped ($\ensuremath{\delta}=0$) ``parent'' state is a quantum spin liquid. In contrast to the relatively short range superconducting (SC) correlations that have been observed in recent studies of the six-leg cylinder in the absence of frustration, we find power-law SC correlations with a Luttinger exponent, ${K}_{\mathrm{SC}}\ensuremath{\approx}1$, consistent with a strongly diverging SC susceptibility, $\ensuremath{\chi}\ensuremath{\sim}{T}^{\ensuremath{-}(2\ensuremath{-}{K}_{\mathrm{SC}})}$ as the temperature $T\ensuremath{\rightarrow}0$. The spin-spin correlations---as in the undoped state---fall exponentially suggesting that the SC ``pairing'' correlations evolve smoothly from the insulating parent state.