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Operator growth in the transverse-field Ising spin chain with integrability-breaking longitudinal field
Physical Review E ( IF 2.4 ) Pub Date : 2021-09-09 , DOI: 10.1103/physreve.104.034112
Jae Dong Noh 1
Affiliation  

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 when the longitudinal field is weak. 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.

中文翻译:

具有可积性破坏纵向场的横向场伊辛自旋链中的算子增长

我们在一维中研究了横向场 Ising 自旋链的算子增长动力学,因为它会改变纵向场的强度。海森堡图中的一个算子在扩展的希尔伯特空间中展开。最近,有人提出传播动力学具有普遍特征,表明潜在量子动力学的混沌性。我们通过数值证明了纵向场存在下的算子增长动力学遵循一维混沌系统的通用标度定律。我们还发现,当纵向场较弱时,算子增长动力学满足交叉标度律。交叉标度确认均匀纵向场使系统在任何非零值处混沌。
更新日期:2021-09-09
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