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Zipper entanglement renormalization on one-dimensional free fermion systems

Ka Chun Pang

Published Jan 1, 2023• 0 citations
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Abstract

991013181659403412 HKUST Electronic Theses Zipper entanglement renormalization on one-dimensional free fermion systems by Pang Ka Chun thesis 2023 1 online resource (xi, 49 pages) : illustrations (some color) The Zipper Entanglement Renormalization(ZER) is a ‘state-based’ description for the free fermion…Read more ›
DOI
10.14711/thesis-991013181659403412

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Zipper Entanglement Renormalization for Free Fermions

Sing Lam Wong, Ka Chun Pang, Hoi Chun Po

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.

arXiv:2206.11761•Jun 23, 2022•0 citations
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.