Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems

2025/07/10 by Kyle Kawagoe, Kawagoe, Kyle, Wilbur Shirley +1 · 3 citations
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Strongly Correlated Electrons (cond-mat.str-el)

paper · pdf · doi:10.48550/arxiv.2507.07430

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

Abstract

We describe a method for computing the anomaly of any finite unitary symmetry group G acting by finite-depth quantum circuits on a two-dimensional lattice system. The anomaly is characterized by an index valued in the cohomology group H⁴(G,U(1)), which generalizes the Else-Nayak index for locality preserving symmetries of quantum spin chains. We show that a nontrivial index precludes the existence of a trivially gapped symmetric Hamiltonian; it is also an obstruction to ``onsiteability" of the symmetry action. We illustrate our method via a simple example with G=ℤ₂×ℤ₂×ℤ₂×ℤ₂. Finally, we provide a diagrammatic interpretation of the anomaly formula which hints at a higher categorical structure.

Citations

• Higher symmetries and anomalies in quantum lattice systems
• Disentangling anomaly-free symmetries of quantum spin chains
• Topological Phases of Many-Body Localized Systems: Beyond Eigenstate Order
• Anomalous symmetries of quantum spin chains and a generalization of the Lieb-Schultz-Mattis theorem
• 1d lattice models for the boundary of 2d "Majorana" fermion SPTs: Kramers-Wannier duality as an exact Z₂ symmetry
• Generalized global symmetries
• Topological interactions in broken gauge theories
• Two soluble models of an antiferromagnetic chain

Cited by

• Onsiteability of Higher-Form Symmetries
• Anyonic membranes and Pontryagin statistics
• Higher-Form Anomalies on Lattices

Related

• Higher symmetries and anomalies in quantum lattice systems
• Anomalous symmetries of quantum spin chains and a generalization of the Lieb-Schultz-Mattis theorem
• Anomaly-free symmetries with obstructions to gauging and onsiteability
• Classification of locality preserving symmetries on spin chains
• Twisted locality-preserving automorphisms, anomaly index, and generalized Lieb-Schultz-Mattis theorems with anti-unitary symmetries