  We extend to a possibly infinite chain the conformally invariant mechanical
system that was introduced earlier as a toy model for understanding the
topological Yang-Mills theory. It gives a topological quantum model that has
interesting and computable zero modes and topological invariants. It confirms
the recent conjecture by several authors that supersymmetric quantum mechanics
may provide useful tools for understanding robotic mechanical systems (Vitelli
et al.) and condensed matter properties (Kane et al.), where trajectories of
effective models are allowed or not by the conservation of topological indices.
The absences of ground state and mass gaps are special features of such
systems.
