  Condensed matter physicists have long sought a realistic two-dimensional (2D)
magnetic system whose ground state is a {\it spin liquid}---a zero temperature
state in which quantum fluctuations have melted away any form of magnetic
order. The nearest-neighbor $S=1/2$ Heisenberg model on the kagome lattice has
seemed an ideal candidate, but in recent years some approximate numerical
approaches to it have yielded instead a valence bond crystal. We have used the
density matrix renormalization group to perform very accurate simulations on
numerous cylinders with circumferences up to 12 lattice spacings, finding
instead of the valence bond crystal a singlet-gapped spin liquid with
substantially lower energy that appears to have $Z_2$ topological order. Our
results, through a combination of very low energy, short correlation lengths
and corresponding small finite size effects, a new rigorous energy bound, and
consistent behavior on many cylinders, provide strong evidence that the 2D
ground state of this model is a gapped spin liquid.
