The effect of non-magnetic impurities is discussed for both the two-leg Heisenberg ladder system and other spin liquids with excitation gap. It is shown that the random depletion of spins introduces a random Berry phase term to the non-linear sigma model. The classical nature of the antiferromagnetic correlation is enhanced by the topological decoherence, and the staggered susceptibility shows more singular behavior at low temperatures than the uniform antiferromagnetic Heisenberg chain.
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