  We study the behaviour of entanglement entropy in two-dimensional CFTs under
Weyl transformations from the Weyl anomaly. Using the Ryu-Takayanagi-formula,
we show that these deformations correspond to local deformations of the IR
cutoff of AdS$_3$, which gives an example of the local validity of the IR/UV
Connection in AdS/CFT. We then use Matrix Product States to demonstrate the
behaviour of entanglement entropy under Weyl transformations in the
two-dimensional free fermion CFT mapped to the XY-model with site-dependent
coupling. We present numerical results for different deformations of the
background and discuss issues arising for the standard DMRG procedure for the
resulting inhomogeneous interactions due to a nontrivial background.
