Entanglement entropy in lattice gauge theories

Understand

We report on the recent progress in theoretical and numerical studies of entanglement entropy in lattice gauge theories.

• It is shown that the concept of quantum entanglement between gauge fields in two complementary regions of space can only be introduced if the Hilbert space of physical states is extended in a certain way.
• In the extended Hilbert space, the entanglement entropy can be partially interpreted as the classical Shannon entropy of the flux of the gauge fields through the boundary between the two regions.
• Such an extension leads to a reduction procedure which can be easily implemented in lattice simulations by constructing lattices with special topology.