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Comment: RevteX, preprint ITP (1994)
Comment: 11 pages, RevteX, preprint ITP
Comment: 9 pages, Revtex, Epsf, 4 figures. To appear in the Proceedings of the Euroconference on "Correlations in unconventional quantum liquids" in Zeitschrift f\"ur Physik B - Condensed Matter (dedicated to the memory of Sir Rudolph Peierls)
Comment: Minor typos corrected
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.
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