Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
Anomalous Sym- metries of Quantum Spin Chains and a Generalization of the Lieb–Schultz–Mattis Theorem
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Lattice CPT symmetry upgrades the Onsager chiral symmetry anomaly from order two to infinite order, better matching the continuum chiral anomaly, with discussion of associated 2+1d SPT phases.
A bosonic lattice model realizes exact chiral symmetry and its anomaly in 3+1d, with the continuum limit a compact boson theory with axion-like coupling.
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Symmetry Spans and Enforced Gaplessness
Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
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Infinite-Order Lattice Chiral Anomalies and CPT
Lattice CPT symmetry upgrades the Onsager chiral symmetry anomaly from order two to infinite order, better matching the continuum chiral anomaly, with discussion of associated 2+1d SPT phases.
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Lattice chiral symmetry from bosons in 3+1d
A bosonic lattice model realizes exact chiral symmetry and its anomaly in 3+1d, with the continuum limit a compact boson theory with axion-like coupling.
- A local description of strong symmetries and strong-to-weak symmetry breaking in quantum many-body systems