出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：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.
This enables us to measure the entanglement entropy in lattice Monte-Carlo simulations. On the
simplest example of Z2 lattice gauge theory in (2+1) dimensions we demonstrate the relation
between entanglement entropy and the classical entropy of the field flux. For SU (2) lattice gauge
theory in four dimensions, we find a signature of non-analytic dependence of the entanglement
entropy on the size of the region. We also comment on the holographic interpretation of the
entanglement entropy.
