  Entanglement renormalization refers to a sequence of real-space
coarse-graining transformations in which short-range entanglement on
successively longer length scales are distilled out. In this work, we introduce
a state-based approach, "zipper entanglement renormalization" (ZER), for
free-fermion systems. The name derives from a unitary we construct at every
renormalization step, dubbed the zipper, which unzips the state into an
approximate tensor product between a short-range entangled state and a
renormalized one carrying the longer-range entanglement. By successively
performing ZER on the renormalized states, we obtain a unitary transformation
of the input state into a state that is approximately factorized over the
emergent renormalization spacetime. As a demonstration, we apply ZER to
one-dimensional models and show that it efficiently disentangles the ground
states of the Su-Schrieffer-Heeger model, a scale-invariant critical state, as
well as a more general gapless state with two sets of Fermi points.
