Entanglement renormalization and wavelets

Understand

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.