Local integrals of motion in many‐body localized systems

By J. Imbrie, V. Ros, Antonello Scardicchio. 2016

255 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/74b4b5521765b7991e7623c0ce20dd4a43785fb3

Citations in the corpus

• Many-body localization: An introduction and selected topics (2017, unknown): “[55, 56], we extract here only the main ideas.”