  The Landau-Zener(LZ) transition of a two-level system coupling to spin chains
near their critical points is studied in this paper. Two kinds of spin chains,
the Ising spin chain and XY spin chain, are considered. We calculate and
analyze the effects of system-chain coupling on the LZ transition. A relation
between the LZ transition and the critical points of the spin chain is
established. These results suggest that LZ transitions may serve as the
witnesses of criticality of the spin chain. This may provide a new way to study
quantum phase transitions as well as LZ transitions.
