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Autori principali: Kim, Isaac H., Ranard, Daniel
Natura: Preprint
Pubblicazione: 2024
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Accesso online:https://arxiv.org/abs/2405.17379
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author Kim, Isaac H.
Ranard, Daniel
author_facet Kim, Isaac H.
Ranard, Daniel
contents We prove the conjectured classification of topological phases in two spatial dimensions with gappable boundary, in a simplified setting. Two gapped ground states of lattice Hamiltonians are in the same quantum phase of matter, or topological phase, if they can be connected by a constant-depth quantum circuit. It is conjectured that the Levin-Wen string-net models exhaust all possible gapped phases with gappable boundary, and these phases are labeled by unitary modular tensor categories. We prove this under the assumption that every phase has a representative state with zero correlation length satisfying the entanglement bootstrap axioms, or a strict form of area law. Our main technical development is to transform these states into string-net states using constant-depth quantum circuits.
format Preprint
id arxiv_https___arxiv_org_abs_2405_17379
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Classifying 2D topological phases: mapping ground states to string-nets
Kim, Isaac H.
Ranard, Daniel
Quantum Physics
Strongly Correlated Electrons
High Energy Physics - Theory
Mathematical Physics
We prove the conjectured classification of topological phases in two spatial dimensions with gappable boundary, in a simplified setting. Two gapped ground states of lattice Hamiltonians are in the same quantum phase of matter, or topological phase, if they can be connected by a constant-depth quantum circuit. It is conjectured that the Levin-Wen string-net models exhaust all possible gapped phases with gappable boundary, and these phases are labeled by unitary modular tensor categories. We prove this under the assumption that every phase has a representative state with zero correlation length satisfying the entanglement bootstrap axioms, or a strict form of area law. Our main technical development is to transform these states into string-net states using constant-depth quantum circuits.
title Classifying 2D topological phases: mapping ground states to string-nets
topic Quantum Physics
Strongly Correlated Electrons
High Energy Physics - Theory
Mathematical Physics
url https://arxiv.org/abs/2405.17379