  We propose an adaptation of Entanglement Renormalization for quantum field
theories that, through the use of discrete wavelet transforms, strongly
parallels the tensor network architecture of the \emph{Multiscale Entanglement
Renormalization Ansatz} (a.k.a. MERA). Our approach, called wMERA, has several
advantages of over previous attempts to adapt MERA to continuum systems. In
particular, (i) wMERA is formulated directly in position space, hence
preserving the quasi-locality and sparsity of entanglers; and (ii) it enables a
built-in RG flow in the implementation of real-time evolution and in
computations of correlation functions, which is key for efficient numerical
implementations. As examples, we describe in detail two concrete
implementations of our wMERA algorithm for free scalar and fermionic theories
in (1+1) spacetime dimensions. Possible avenues for constructing wMERAs for
interacting field theories are also discussed.
