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arXiv · 1402.1421

An Explicit Bound for Dynamical Localisation in an Interacting Many-Body System

P. -L. Giscard·Z. Choo·M. T. Mitchison·J. J. Mendoza-Arenas·D. Jaksch
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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.

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P. -L. Giscard, Z. Choo, M. T. Mitchison, J. J. Mendoza-Arenas, D. Jaksch. 2014-02-06. An Explicit Bound for Dynamical Localisation in an Interacting Many-Body System. https://arxiv.org/abs/1402.1421

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