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

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arxiv 2405.17379 v1 pith:GJWCFWAZ submitted 2024-05-27 quant-ph cond-mat.str-elhep-thmath-phmath.MP

classification quant-phcond-mat.str-elhep-thmath-phmath.MP
keywords phasesstatesphasequantumtopologicalboundaryconjecturedconstant-depth
verification ladder T0 review T1 audit T2 compute T3 formal
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Many-body chirality of topological stabilizer states

    quant-ph 2026-06 unverdicted novelty 7.0 of 10

    Many-body chirality for Z_d^(k) stabilizer states equals mirror non-invariance of anyon data, is intrinsically four-partite, and states with d>2 also show intrinsic imaginarity not removable by local unitaries.

  2. Long-range nonstabilizerness of topologically encoded states from mutual information

    quant-ph 2026-05 unverdicted novelty 6.0 of 10

    Mutual information between non-contractible regions on the torus fully classifies long-range nonstabilizerness for toric-code states but leaves a finite subset undetected in the doubled-Fibonacci string-net model.

  3. Toward Entanglement Bootstrap for Conformal Field Theory in Any Dimension

    hep-th 2026-06 unverdicted novelty 5.0 of 10

    Proposes and numerically tests a reconstructed Hamiltonian for approximate CFT ground states in any dimension that recovers CFT spectral properties.

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