Many-Body Localization: Concepts and Simple Models

Abstract

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-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.

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Cited by in corpus (5)

• Localization Properties of the XY Spin Chain. A review of mathematical results with an eye toward Many-Body Localization
• Decay of correlations and absence of superfluidity in the disordered Tonks-Girardeau gas
• On transport properties of isotropic quasiperiodic $XY$ spin chains
• Experimental tests of Lieb-Robinson bounds
• Bounding entanglement spreading after a local quench