A complete set of local integrals of motion (LIOM) is a key concept for describing many-body localization (MBL), which explains a variety of intriguing phenomena in MBL systems. For example, LIOM constrain the dynamics and result in ergodicity violation and breakdown of the eigenstate thermalization hypothesis. However, it is difficult to find a complete set of LIOM explicitly and accurately in practice, which impedes some quantitative structural characterizations of MBL systems. Here we propose an accurate numerical method for constructing LIOM, discover through the LIOM an interaction-induced characteristic length $\xi_+$, and prove a 'quasi-product-state' structure of the eigenstates with that characteristic length $\xi_+$ for MBL systems. More specifically, we find that there are two characteristic lengths in the LIOM. The first one is governed by disorder and is of Anderson-localization nature. The second one is induced by interaction but shows a discontinuity at zero interaction, showing a nonperturbative nature. We prove that the entanglement and correlation in any eigenstate extend not longer than twice the second length and thus the eigenstates of the system are the quasi-product states with such a localization length.
Supported by the National Natural Science Foundation of China under Grant Nos 11474356 and 91421304, and the Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase) under Grant No U1501501. R.Q.H. was supported by China Postdoctoral Science Foundation under Grant No 2015T80069. Computational resources were provided by National Supercomputer Center in Guangzhou with Tianhe-2 Supercomputer and Physical Laboratory of High Performance Computing in RUC.
- Rong-Qiang He, Zhong-Yi Lu. Interaction-Induced Characteristic Length in Strongly Many-Body Localized Systems[J]. CPL, 2018, 35(2): 027101.