Many-body localisation implies that eigenvectors are matrix-product states

Abstract

The phenomenon of many-body localisation received a lot of attention recently, both for its implications in condensed-matter physics of allowing systems to be an insulator even at non-zero temperature as well as in the context of the foundations of quantum statistical mechanics, providing examples of systems showing the absence of thermalisation following out-of-equilibrium dynamics. In this work, we establish a novel link between dynamical properties - the absence of a group velocity and transport - with entanglement properties of individual eigenvectors. Using Lieb-Robinson bounds and filter functions, we prove rigorously under simple assumptions on the spectrum that if a system shows strong dynamical localisation, all of its many-body eigenvectors have clustering correlations. In one dimension this implies directly an entanglement area law, hence the eigenvectors can be approximated by matrix-product states. We also show this statement for parts of the spectrum, allowing for the existence of a mobility edge above which transport is possible.

13 pages, 4 figures

References in corpus (15)

• The density-matrix renormalization group in the age of matrix product states
• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• Localization of interacting fermions at high temperature
• Many body localization in Heisenberg XXZ magnet in a random field
• Matrix product states represent ground states faithfully
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Constructing local integrals of motion in the many-body localized phase
• Absence of Thermalization in Nonintegrable Systems
• Propagation of Correlations in Quantum Lattice Systems
• General entanglement scaling laws from time evolution
• Entanglement spreading in a many-body localized system
• The computational difficulty of finding MPS ground states
• Quasi-adiabatic Continuation for Disordered Systems: Applications to Correlations, Lieb-Schultz-Mattis, and Hall Conductance

Cited by in corpus (8)

• Spectral tensor networks for many-body localization
• Explicit construction of local conserved operators in disordered many-body systems
• Many-Body Localization in System with a Completely Delocalized Single-Particle Spectrum
• Experimental tests of Lieb-Robinson bounds
• Insights from Quantum Information into Fundamental Physics
• Droplet localization in the random XXZ model and its manifestations
• Many-body localization with mobility edges
• Bounding entanglement spreading after a local quench