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

TL;DR

This study numerically investigates the entanglement entropy in SU(2) lattice gauge theory, revealing nonanalytic behavior and phase transition signatures consistent with predictions from AdS/CFT correspondence.

Contribution

It provides the first numerical evidence of nonanalytic entanglement entropy behavior in SU(2) lattice gauge theory, supporting theoretical predictions from large N_c gauge theories.

Findings

Detected nonanalytic behavior of entanglement entropy at a critical length l_c.

Observed that the derivative of entanglement entropy with respect to l likely has a discontinuity.

Confirmed the presence of a quadratically divergent, l-independent term in the entropy.

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.