Studio su reticolo dell'entropia di entanglement nella teoria di Yang-Mills

The quantum entanglement of states of systems with many degrees of freedom is a very useful, model-independent, physical property, characterizing the structure of the ground state of quantum fields. It can be used to classify different phases of field theories, which are associated with different patterns of entanglement. In this work, we carry out a high-precision non-perturbative study of the behaviour of the entanglement entropy in SU(2) Yang-Mills theory in 3+1 dimensions. We regularize the theory on a Euclidean hypercubic lattice of spacing a, which automatically provides a gauge-invariant momentum cut-off O(a^{-1}). We focus on the entanglement between a 3-dimensional slab of thickness l and its complement, and investigate quantitatively the quadratically ultra-violet divergent, l-independent, contribution to the entanglement entropy, as well as the non-divergent terms, scaling like l^{-2}