total Hilbert space can be written as a direct product $H=H_A \otimes H_B$. Denoting by $\rho$ the density matrix characterizing the state of the system, the reduced density matrix associated to $A$ is obtained by tracing $\rho$ over the degrees of freedom of $B$, i.e. $\rho_A = \textrm{Tr}_B \rho$. Then, the entanglement entropy is defined as the corresponding Von Neumann entropy, namely $S_A = -  \,\textrm{Tr}_A(\rho_A \log \rho_A)$. When the system is in a pure state, we have $\rho = | \Psi \rangle \langle \Psi |$ and $S_A = S_B$. A very interesting situation occurs when $A$ and $B$ correspond to a spatial bipartition of the system. In this case the entanglement entropy is called geometric entropy. Here we consider this quantity and we will always refer to it as the entanglement entropy. Its interesting feature is that is satisfies the so called area law: the leading term in the expansion for small UV cutoff $a$ is proportional to the area of the boundary separating $A$ and $B$. In $d$ spatial dimensions we have $S_A \propto \textrm{Area}(\partial A)/a^{d-1}+ \dots$, where the dots represent higher order terms in $a$ [@Srednicki:1993im]. This area law is violated in two dimensional conformal field theories, 