Comparing many-body localization lengths via nonperturbative construction of local integrals of motion

• Main Authors: Peng, Pai (Author), Li, Zeyang (Author), Yan, Haoxiong (Author), Wei, Xuan (Author), Cappellaro, Paola (Author)
• Other Authors: Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor), Massachusetts Institute of Technology. Research Laboratory of Electronics (Contributor), Massachusetts Institute of Technology. Department of Physics (Contributor), Massachusetts Institute of Technology. Department of Nuclear Science and Engineering (Contributor)
• Format: Article
• Language: English
• Published: American Physical Society (APS), 2020-02-25T15:50:51Z.
• Subjects: Article
• Online Access: Get fulltext

 Many-body localization (MBL), characterized by the absence of thermalization and the violation of conventional thermodynamics, has elicited much interest both as a fundamental physical phenomenon and for practical applications in quantum information. A phenomenological model which describes the system using a complete set of local integrals of motion (LIOMs) provides a powerful tool to understand MBL but can usually be computed only approximately. Here we explicitly compute a complete set of LIOMs with a nonperturbative approach by maximizing the overlap between LIOMs and physical spin operators in real space. The set of LIOMs satisfies the desired exponential decay of the weight of LIOMs in real space. This LIOM construction enables a direct mapping from the real-space Hamiltonian to the phenomenological model and thus enables studying the localized Hamiltonian and the system dynamics. We can thus study and compare the localization lengths extracted from the LIOM weights, their interactions, and dephasing dynamics, revealing interesting aspects of many-body localization. Our scheme is immune to accidental resonances and can be applied even at the phase transition point, providing a tool to study the microscopic features of the phenomenological model of MBL.