2016/09/30 by John Z. Imbrie, J. Z. Imbrie, Valentina Ros +3 · 6 citations
Engineering · Mathematics · Physics and Astronomy · #Complex system #Control and Stability of Dynamical Systems #Hamiltonian (control theory) #Hamiltonian system #Motion (physics) #Phenomenology (philosophy) #Quantum chaos and dynamical systems #Quantum many-body systems #Set (abstract data type) #cond-mat.dis-nn #math-ph #math.MP
paper · pdf · doi:10.1002/andp.201600278
Updated version with references added. Review for the special issue on "Many-Body Localization" in Annalen der Physik. Comments are welcome
openalex created_date 2016/10/07 · arxiv created 2016/10/27 · openalex publication_date 2017/05/11 · arxiv updated 2017/08/02 · openalex updated_date 2026/08/06
We review the current (as of Fall 2016) status of the studies on the emergent integrability in many‐body localized models. We start by explaining how the phenomenology of fully many‐body localized systems can be recovered if one assumes the existence of a complete set of (quasi)local operators which commute with the Hamiltonian (local integrals of motions, or LIOMs). We describe the evolution of this idea from the initial conjecture, to the perturbative constructions, to the mathematical proof given for a disordered spin chain. We discuss the proposed numerical algorithms for the construction of LIOMs and the status of the debate on the existence and nature of such operators in systems with a many‐body mobility edge, and in dimensions larger than one. image