Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2

Understand

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.