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Extracting Wilson loop operators and fractional statistics from a single bulk ground state

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arxiv 2209.14302 v2 pith:MWE7GL5G submitted 2022-09-28 cond-mat.str-el quant-ph

classification cond-mat.str-elquant-ph
keywords operatorsgroundloopstatewilsonfunctionsingletopological
verification ladder T0 review T1 audit T2 compute T3 formal
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An essential aspect of topological phases of matter is the existence of Wilson loop operators that keep the ground state subspace invariant. Here we present and implement an \it unbiased \rm numerical optimization scheme to systematically find the Wilson loop operators given a single ground state wave function of a gapped Hamiltonian on a disk. We then show how these Wilson loop operators can be cut and glued through further optimization to give operators that can create, move, and annihilate anyon excitations. We subsequently use these operators to determine the braiding statistics and topological twists of the anyons, yielding a way to fully extract topological order from a single wave function. We apply our method to the ground state of the perturbed toric code and doubled semion models with a magnetic field that is up to a half of the critical value. From a contemporary perspective, this can be thought of as a machine learning approach to discover emergent 1-form symmetries of a ground state wave function. From an application perspective, our approach can be relevant to find Wilson loop operators in current quantum simulators.

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Cited by 4 Pith papers

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

  1. Microscopic universal theory of symmetry-enriched topological quantum spin liquids

    cond-mat.str-el 2026-06 unverdicted novelty 7.0 of 10

    A new framework maps microscopic inputs to universal properties of generic symmetry-enriched TQSLs and establishes a bijective crystalline equivalence principle between lattice-plus-internal and internal-only symmetry data.

  2. From Multipartite Entanglement to TQFT

    hep-th 2026-02 conditional novelty 7.0 of 10

    Genuine multipartite entanglement of a gapped ground state is conjectured and, for Levin-Wen models, shown to reproduce the TQFT partition function on any 3-manifold.

  3. 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.

  4. Crystalline topological invariants in quantum many-body systems

    cond-mat.str-el 2026-04 unverdicted novelty 1.0 of 10

    Reviews characterization, classification, and detection of crystalline symmetry-protected topological invariants in 2D integer and fractional Chern insulators, focusing on translation, rotation, and charge conservation.

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