Numerical study of entanglement entropy in SU(2)SU(2) lattice gauge theory

The entropy of entanglement between a three-dimensional slab of thickness l   and its complement is studied numerically for four-dimensional SU(2)SU(2) lattice gauge theory. We find a signature of a nonanalytic behavior of the entanglement entropy, which was predicted recently for large NcNc confining gauge theories in the framework of AdS/CFT correspondence. The derivative of the entanglement entropy over l   is likely to have a discontinuity at some l=lcl=lc. It is argued that such behavior persists even at finite temperatures, probably turning into a sort of crossover for temperatures larger than the temperature of the deconfinement phase transition. We also confirm that the entanglement entropy contains quadratically divergent l  -independent term, and that the nondivergent terms behave as l−2l−2 at small distances.