  We show that macroscopic nonintegrable lattices of spins 1/2, which are often
considered to be chaotic, do not exhibit the basic property of classical
chaotic systems, namely, exponential sensitivity to small perturbations. We
compare chaotic lattices of classical spins and nonintegrable lattices of spins
1/2 in terms of their magnetization responses to imperfect reversal of spin
dynamics known as Loschmidt echo. In the classical case, magnetization exhibits
exponential sensitivity to small perturbations of Loschmidt echoes, which is
characterized by twice the value of the largest Lyapunov exponent of the
system. In the case of spins 1/2, magnetization is only power-law sensitive to
small perturbations. Our findings imply that it is impossible to define
Lyapunov exponents for lattices of spins 1/2 even in the macroscopic limit. At
the same time, the above absence of exponential sensitivity to small
perturbations is an encouraging news for the efforts to create quantum
simulators. The power-law sensitivity of spin 1/2 lattices to small
perturbations is predicted to be measurable in nuclear magnetic resonance
experiments.
