  We study the out-of-time-order correlators (OTOC) of Skyrmion as baryon in
the D0-D4/D8 model which is holographically dual to QCD with an non-zero theta
angle. The baryon state is identified to the excitation of the Skyrmion which
is described by a quantum mechanical system in holography. By employing the
definition of OTOC in quantum mechanics, we derive the formulas and demonstrate
explicitly the numerical calculations of the OTOC. Our calculation illustrates
the quantum OTOC with imaginary Lyapunov coefficient indicates the possibly
metastable baryonic status in the presence of the theta angle while the
classical OTOC can not, thus it reveals the theta-dependent features of QCD are
dominated basically by its quantum properties. Furthermore, the OTOC also
implies the baryonic phase becomes really chaotic with real Lyapunov exponent
if the theta angle increases sufficiently which agrees with the unstable baryon
spectrum presented in this model. In this sense, we believe the OTOC may be
treated as a tool to detect the baryonic phase structure of QCD.
