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Superconductivity in doped quantum paramagnets has been a subject of longtheoretical inquiry. In this work we report a density matrix renormalizationgroup study of lightly doped $t$-$J$ models on the square lattice (doped holedensities $\delta = 1/12$ and 1/8) with parameters for which previous studieshave suggested that the undoped system in 2D is either a quantum spin liquid ora valence bond crystal. Our studies are performed on cylinders with width up to8. Ground-state correlations are found to be nearly identical for the ``dopedquantum spin liquid'' and ``doped valence bond crystal''. Upon increasing thecylinder width from 4 to 8, we observed a significant strengthening of thequasi-long-range superconducting correlations, and a dramatic suppression ofany ``competing'' charge-density-wave order. Extrapolating from the observedbehavior of the width 8 cylinders, we speculate that the system has a nodelessd-wave superconducting ground-state in the 2D limit.

Superconducting valence bond fluid in lightly doped 8-leg $t$-$J$ cylinders