Abstract:
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.
