An Explicit Bound for Dynamical Localisation in an Interacting Many-Body System
Abstract
We characterise and study dynamical localisation of a finite interacting quantum many-body system. We present explicit bounds on the disorder strength required for the onset of localisation of the dynamics of arbitrary ensemble of sites of the XYZ spin-1/2 model. We obtain these results using a novel form of the fractional moment criterion, which we establish, together with a generalisation of the self-avoiding walk representation of the system Green's functions, called path-sums. These techniques are not specific to the XYZ model and hold in a much more general setting. We further present bounds for two observable quantities in the localised regime: the magnetisation of any sublattice of the system as well as the linear magnetic response function of the system. We confirm our results through numerical simulations.
Cite
@article{arxiv.1402.1421,
title = {An Explicit Bound for Dynamical Localisation in an Interacting Many-Body System},
author = {P. -L. Giscard and Z. Choo and M. T. Mitchison and J. J. Mendoza-Arenas and D. Jaksch},
journal= {arXiv preprint arXiv:1402.1421},
year = {2014}
}
Comments
35 pages; 5 figures