Non-magnetic impurities in S=1/2 spin-Peierls system and Heisenberg ladder systems

In this paper we study the effect of non-magnetic impurities in spin-Peierls system $CuGeO_3$ within the framework of non-linear sigma model plus topological term. We show that local moments are induced in both the $Zn$-doped and $Si$-doped $CuGeO_3$ compounds. Effective low energy theories for the impurity-induced local moments are derived in both cases where interesting differences between the two cases and between the $Zn$-doped Heisenberg two-ladder system are pointed out. The low-energy physics of the $Zn$-doped Heisenberg three-leg ladder system is also discussed.