Droplet localization in the random XXZ model and its manifestations

Abstract

We examine many-body localization properties for the eigenstates that lie in the droplet sector of the random-field spin-$\frac{1}{2}$ XXZ chain. These states satisfy a basic single cluster localization property (SCLP), derived in \cite{EKS}. This leads to many consequences, including dynamical exponential clustering, non-spreading of information under the time evolution, and a zero velocity Lieb Robinson bound. Since SCLP is only applicable to the droplet sector, our definitions and proofs do not rely on knowledge of the spectral and dynamical characteristics of the model outside this regime. Rather, to allow for a possible mobility transition, we adapt the notion of restricting the Hamiltonian to an energy window from the single particle setting to the many body context.

6 pages, no figures

References in corpus (8)

• 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
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Propagation of Correlations in Quantum Lattice Systems
• Many-body localisation implies that eigenvectors are matrix-product states
• Emergent local integrals of motion without a complete set of localized eigenstates