Rigorous free fermion entanglement renormalization from wavelet theory

Understand

We construct entanglement renormalization schemes which provably approximate the ground states of non-interacting fermion nearest-neighbor hopping Hamiltonians on the one-dimensional discrete line and the two-dimensional square lattice.

• These schemes give hierarchical quantum circuits which build up the states from unentangled degrees of freedom.
• The circuits are based on pairs of discrete wavelet transforms which are approximately related by a "half-shift": translation by half a unit cell.
• The presence of the Fermi surface in the two-dimensional model requires a special kind of circuit architecture to properly capture the entanglement in the ground state.