Classifying 2D topological phases: mapping ground states to string-nets

• URL: http://arxiv.org/abs/2405.17379v1
• Date: Mon, 27 May 2024 17:36:17 GMT
• Title: Classifying 2D topological phases: mapping ground states to string-nets
• Authors: Isaac H. Kim, Daniel Ranard,
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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