Entanglement and criticality in translational invariant harmonic lattice systems with finite-range interactions
Abstract
We discuss the relation between entanglement and criticality in translationally invariant harmonic lattice systems with non-randon, finite-range interactions. We show that the criticality of the system as well as validity or break-down of the entanglement area law are solely determined by the analytic properties of the spectral function of the oscillator system, which can easily be computed. In particular for finite-range couplings we find a one-to-one correspondence between an area-law scaling of the bi-partite entanglement and a finite correlation length. This relation is strict in the one-dimensional case and there is strog evidence for the multi-dimensional case. We also discuss generalizations to couplings with infinite range. Finally, to illustrate our results, a specific 1D example with nearest and next-nearest neighbor coupling is analyzed.
Keywords
Cite
@article{arxiv.quant-ph/0506169,
title = {Entanglement and criticality in translational invariant harmonic lattice systems with finite-range interactions},
author = {R. G. Unanyan and M. Fleischhauer},
journal= {arXiv preprint arXiv:quant-ph/0506169},
year = {2009}
}
Comments
4 pages, one figure, revised version