Disentangling anomaly-free symmetries of quantum spin chains

2025/03/12 by Sahand Seifnashri, Seifnashri, Sahand, Wilbur Shirley +1 · 6 citations
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Physics of Superconductivity and Magnetism #Quantum Physics (quant-ph) #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el) #Topological Materials and Phenomena

paper · doi:10.48550/arxiv.2503.09717

openalex publication_date 2025/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ancillae 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 ancillae. 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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