  We study the dynamics of a single hole in Li and Sr doped La$_{2}$CuO$_4$ and
its extension to a finite hole concentration. We compare the physics of
La$_{2-x}$Sr$_x$CuO$_4$ and La$_{2}$Cu$_{1-x}$Li$_x$O$_4$ and explain why these
systems are remarkably different. We demonstrate that holes in
La$_{2}$Cu$_{1-x}$Li$_x$O$_4$ are always localized and that there is a critical
concentration, $x_c\approx 0.03$, above which the holes break the global
antiferromagnetic state into an array of weakly coupled antiferromagnetic
clusters (antiferromagnetic shards). We show that the spin-shard state provides
a description of the magnetic and electric properties of
La$_{2}$Cu$_{1-x}$Li$_x$O$_4$. Two experiments that can test our theory are
proposed.
