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Disentangling anomaly-free symmetries of quantum spin chains

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arxiv 2503.09717 v1 pith:IIPA7IMY submitted 2025-03-12 cond-mat.str-el hep-thquant-ph

Sahand Seifnashri , Wilbur Shirley This is my paper
classification cond-mat.str-elhep-thquant-ph
keywords anomaly-freeon-sitesymmetriessymmetryancillascircuitdisentanglinghamiltonian
verification ladder T0 review T1 audit T2 compute T3 formal
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We clarify the lore that anomaly-free symmetries are either on-site or can be transformed into on-site symmetries. We prove that any finite, internal, anomaly-free symmetry in a 1+1d lattice Hamiltonian system can be disentangled into an on-site symmetry by introducing ancillas and applying conjugation via a finite-depth quantum circuit. We provide an explicit construction of the disentangling circuit using Gauss's law operators and emphasize the necessity of adding ancillas. Our result establishes the converse to a generalized Lieb-Schultz-Mattis theorem by demonstrating that any anomaly-free symmetry admits a trivially gapped Hamiltonian.

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Cited by 4 Pith papers

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

  1. Exactly Solvable 1+1d Chiral Lattice Gauge Theories

    hep-th 2026-01 conditional novelty 7.0 of 10

    Anomaly-free chiral U(1) gauge theories in 1+1 dimensions can be written as quadratic, exactly solvable lattice Hamiltonians, with the 34-50 model as an explicit example.

  2. Trading Mathematical for Physical Simplicity: Bialgebraic Structures in Matrix Product Operator Symmetries

    quant-ph 2025-09 conditional novelty 7.0 of 10

    MPO symmetries are governed by pre-bialgebras; the anomalous Z2 symmetry of the XX model yields a non-semisimple representation category and new mixed-state fixed points.

  3. Anomaly-free symmetries with obstructions to gauging and onsiteability

    cond-mat.str-el 2025-07 conditional novelty 7.0 of 10

    A new class of two-dimensional lattice symmetries is anomaly-free yet obstructs both gauging and on-site realization, with the obstruction classified by H^2(G,Q+).

  4. Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems

    cond-mat.str-el 2025-07 conditional novelty 7.0 of 10

    A symmetry-restriction procedure computes the H^4(G,U(1)) anomaly class of any finite unitary symmetry acting by finite-depth circuits on a 2D lattice, with nontrivial class forbidding a symmetric invertible gapped state.

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