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arXiv · 1702.05368

Entanglement area laws for long-range interacting systems

Zhe-Xuan Gong·Michael Foss-Feig·Fernando G. S. L. Brandão·Alexey V. Gorshkov
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Abstract

We prove that the entanglement entropy of any state evolved under an arbitrary $1/r^α$ long-range-interacting D-dimensional lattice spin Hamiltonian cannot change faster than a rate proportional to the boundary area for any $α>D+1$. We also prove that for any $α>2D+2$, the ground state of such a Hamiltonian satisfies the entanglement area law if it can be transformed along a gapped adiabatic path into a ground state known to satisfy the area law. These results significantly generalize their existing counterparts for short-range interacting systems, and are useful for identifying dynamical phase transitions and quantum phase transitions in the presence of long-range interactions.

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Zhe-Xuan Gong, Michael Foss-Feig, Fernando G. S. L. Brandão, Alexey V. Gorshkov. 2017-02-17. Entanglement area laws for long-range interacting systems. https://doi.org/10.1103/physrevlett.119.050501

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