  We establish a precise connection between discrete wavelet transforms (WTs)
and entanglement renormalization (ER), a real-space renormalization group
transformation for quantum systems on the lattice, in the context of free
particle systems. Specifically, we employ Daubechies wavelets to build
approximations to the ground state of the critical Ising model, then
demonstrate that these states correspond to instances of the multi-scale
entanglement renormalization ansatz (MERA), producing the first known analytic
MERA for critical systems.
