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

Abstract

The entropy of entanglement between a three-dimensional slab of thickness l and its complement is studied numerically for four-dimensional SU(2) lattice gauge theory. We find a signature of a nonanalytic behavior of the entanglement entropy, which was predicted recently for large N_c 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 = l_c. 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 the inverse square of l at small distances.

arXiv comment10 pages RevTeX, 8 figures, 1 table. Major revision of the introductory section, several references added, some plots updated

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