  We investigate the operator growth dynamics of the transverse field Ising
spin chain in one dimension as varying the strength of the longitudinal field.
An operator in the Heisenberg picture spreads in the extended Hilbert space.
Recently, it has been proposed that the spreading dynamics has a universal
feature signaling chaoticity of underlying quantum dynamics. We demonstrate
numerically that the operator growth dynamics in the presence of the
longitudinal field follows the universal scaling law for one-dimensional
chaotic systems. We also find that the operator growth dynamics satisfies a
crossover scaling law as the longitudinal field turns on. The crossover scaling
confirms that the uniform longitudinal field makes the system chaotic at any
nonzero value. We also discuss the implication of the crossover scaling on the
thermalization dynamics and the effect of a nonuniform local longitudinal
field.
