The effect of nonmagnetic impurities in the two-leg Heisenberg ladder
system and other spin liquids with excitation gap is discussed. It is
shown that the random depletion of spins introduces a random Berry pha
se term into the nonlinear sigma model. The classical nature of the an
tiferromagnetic correlation is enhanced by the topological decoherence
, and the staggered susceptibility shows more singular behavior at low
temperatures than the uniform antiferromagnetic Heisenberg chain.