标题： 多体局域化系统中反序时间对易子的典型增长行为 显示英文标题

标题： Typical growth behavior of the out-of-time-ordered commutator in many-body localized systems

摘要： 我们研究了在随机无序实现在多体局域（MBL）量子自旋链中的反时序对易子（OTOC）增长行为的典型性。 在Heisenberg XXZ链的MBL相中，我们发现OTOC的估计值在主要增长的中间时间随着无序实现显著波动。 尽管在MBL相中无序平均方法失效，但我们认为可以通过遍历各个无序实现来识别OTOC增长的特征行为。 我们发现，在一个依赖于无序的弛豫期之后，通常会出现类似幂律的增长行为，这非常接近在完全MBL系统的有效哈密顿量中推导出的$t^2$形式。 在单个无序实现中观察到的特征增长行为在各种状态制备的测试中是稳健的，并且在均匀纵向场中的随机横场量子Ising链的另一个MBL系统中得到了验证。 显示英文摘要

摘要： We investigate the typicality of the growth behavior of the out-of-time-ordered commutator (OTOC) in the many-body localized (MBL) quantum spin chains across random disorder realizations. In the MBL phase of the Heisenberg XXZ chain, we find that the estimate of the OTOC fluctuates significantly with the disorder realizations at the intermediate times of the main growth. Despite the consequent failure of the disorder average in the MBL phase, we argue that the characteristic behavior of the OTOC growth can still be identified by going through individual disorder realizations. We find that a power-law-type growth behavior appears typically after a disorder-dependent relaxation period, which is very close to the $t^2$ form derived in the effective Hamiltonian of a fully MBL system. The characteristic growth behavior observed at an individual disorder realization is robust in our tests with various state preparations and also verified in another MBL system of the random-transverse-field quantum Ising chain in a uniform longitudinal field.