Disentangling anomaly-free symmetries of quantum spin chains

• URL: http://arxiv.org/abs/2503.09717v1
• Date: Wed, 12 Mar 2025 18:08:22 GMT
• Title: Disentangling anomaly-free symmetries of quantum spin chains
• Authors: Sahand Seifnashri, Wilbur Shirley,
• Abstract summary: We prove that any finite, internal, anomaly-free symmetry in a 1+1d lattice Hamiltonian system can be disentangled into an on-site symmetry.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: 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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