Generalizes LSM theorem to hyperbolic lattices with Fuchsian symmetry and derives lower bound on ground-state degeneracy versus filling and geometry.
Lieb-Schultz-Mattis Anomalies and Anomaly Matching
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abstract
Lieb-Schultz-Mattis (LSM) anomalies are powerful symmetry-based constraints on the correlation, entanglement and dynamics of quantum many-body systems. In this review, we discuss various LSM anomalies and anomaly matching. We start with a pedagogical introduction to these subjects in quantum spin chains, and then generalize the discussion to higher dimensions and other systems. Besides covering the topics related to the standard LSM anomalies, we also review LSM anomalies in disordered systems where the lattice symmetries are only preserved on average, fermionic systems, and systems where the symmetric short-range entangled states are possible but must be nontrivial symmetry-protected topological phases.
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cond-mat.str-el 2years
2026 2verdicts
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The Ising fusion category lattice model features a symmetric critical phase equivalent to the Ising model, a categorical ferromagnetic phase with threefold degeneracy, and a critical categorical antiferromagnetic phase with fourfold degeneracy described by an Ising CFT.
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Lieb-Schultz-Mattis constraints for hyperbolic lattices
Generalizes LSM theorem to hyperbolic lattices with Fuchsian symmetry and derives lower bound on ground-state degeneracy versus filling and geometry.
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Symmetry breaking phases and transitions in an Ising fusion category lattice model
The Ising fusion category lattice model features a symmetric critical phase equivalent to the Ising model, a categorical ferromagnetic phase with threefold degeneracy, and a critical categorical antiferromagnetic phase with fourfold degeneracy described by an Ising CFT.