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Abstract: We report on the recent progress in theoretical and numerical studies ofentanglement entropy in lattice gauge theories. It is shown that the concept ofquantum entanglement between gauge fields in two complementary regions of spacecan only be introduced if the Hilbert space of physical states is extended in acertain way. In the extended Hilbert space, the entanglement entropy can bepartially interpreted as the classical Shannon entropy of the flux of the gaugefields through the boundary between the two regions. Such an extension leads toa reduction procedure which can be easily implemented in lattice simulations byconstructing lattices with special topology. This enables us to measure theentanglement entropy in lattice Monte-Carlo simulations. On the simplestexample of Z2 lattice gauge theory in 2 + 1 dimensions we demonstrate therelation between entanglement entropy and the classical entropy of the fieldflux. For SU2 lattice gauge theory in four dimensions, we find a signature ofnon-analytic dependence of the entanglement entropy on the size of the region.We also comment on the holographic interpretation of the entanglement entropy.

Autor: P. V. Buividovich, M. I. Polikarpov

Fuente: https://arxiv.org/

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