10 August 2021 Tue 4 pm

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We present the operator growth dynamics of the transverse field Ising spin chain in one dimension as varying the strength of the longitudinal field which breaks the integrability.  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 the one-dimensional chaotic systems. We also find that the operator growth dynamics satisfies a crossover scaling law when the longitudinal field is small. 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 prethermalization dynamics and the effect of a nonuniform local longitudinal field.

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