Bosonic entanglement renormalization circuits from wavelet theory

Entanglement renormalization is a unitary real-space scheme. The corresponding quantum circuits or tensor networks are known as MERA, and they particularly well-suited to describing systems at criticality. In this work we show how construct Gaussian bosonic that implement entanglement for ground states of arbitrary free chains. construction based on wavelet theory, the dispersion relation Hamiltonian translated into filter design problem. We give general algorithm approximately solves problem provide an approximation theory relates properties filters accuracy circuits. Finally, explain continuum limit (a field) emerges naturally from construction.