Many-Body Localization: Concepts and Simple Models
2015, v.21, Issue 3, 791-822
We review recent results on many-body localization for two explicitly analyzable models of many-body quantum systems, the XY spin chain in transversal magnetic field as well as interacting systems of harmonic quantum oscillators. In both models the presence of disorder leads to dynamical localization in the form of zero-velocity Lieb\tire Robinson bounds and to exponential decay of ground state correlations. Moreover, for oscillator systems one can also show exponential decay of thermal states as well as an area law bound for the entanglement entropy of ground and thermal states. The key fact which allows a rigorous analysis of these models is that they are given by many-body Hamiltonians which can be reduced to effective single particle Hamiltonians.
Keywords: many-body localization, XY spin chain, quantum oscillator systems, Lieb\tire Robinson bounds, area law