Tensor networks and conformal field theory on the lattice

 The multi-scale entanglement renormalization ansatz (MERA) has been shown over the last 10 years to offer an accurate description of ground states of quantum critical lattice Hamiltonians in 1+1 spacetime dimensions. It has also been conjectured to be a lattice realization of the AdS/CFT correspondence. In this talk I will describe how MERA defines global and local scale transformations on the lattice, and related notions of invariance / covariance under these transformations. Accordingly, we will see that the ground state of the quantum Ising spin chain is scale invariant (in spite of the presence of an explicit length scale -- the lattice spacing!). Under local scale transformations, we will also see that the low energy subspace of the lattice model transforms without mixing states in different conformal towers, as expected.