Zipper Entanglement Renormalization for Free Fermions

TL;DR

This paper introduces zipper entanglement renormalization (ZER), a novel state-based method for disentangling free-fermion ground states across scales, demonstrated on 1D models including critical and gapless states.

Contribution

ZER provides a new unitary-based approach to efficiently disentangle free-fermion states by unzipping short-range entanglement at each renormalization step.

Findings

Successfully disentangles ground states of the Su-Schrieffer-Heeger model

Efficiently handles scale-invariant critical states

Effective on gapless states with multiple Fermi points

Abstract

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.