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

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.Comment: 4 pages, one figure, revised versio

DIGITAL TECHNOLOGIES IN THE OIL AND GAS INDUSTRY

The issues of changing the traditional activities of enterprises towards the use of digital technologies have been considered. The results of studies of the implementation of digital technologies in the activities of companies in the oil and gas industry have been adduced. The technologies of intellectual wells, intellectual fields, deserted hydrocarbon production, which form the digital oil and gas industry, have been reviewed. The practice of applying digital technologies in the domestic and foreign fuel and energy complexes has been analyzed. Current trends in the development of digital technologies for the oil and gas industry have been identified. The obstacles, encountered in the development of the oil and gas sector, have been investigated