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Entanglement and criticality in translational invariant harmonic lattice systems with finite-range interactions

R. G. Unanyan·M. Fleischhauer
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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.

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R. G. Unanyan, M. Fleischhauer. 2005-10-13. Entanglement and criticality in translational invariant harmonic lattice systems with finite-range interactions. https://doi.org/10.1103/physrevlett.95.260604

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