Modulated symmetries from generalized Lieb-Schultz-Mattis anomalies

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Abstract
Symmetries rigidly delimit the landscape of quantum matter. Recently uncovered spatially modulated symmetries, whose actions vary with position, enable excitations with restricted mobility, while Lieb-Schultz-Mattis (LSM) type anomalies impose sharp constraints on which lattice phases are realizable. In a one-dimensional spin chain, gauging procedures have linked modulated symmetry to LSM type anomaly, but a general understanding beyond 1D remains incomplete. We show that generalized LSM anomalies force the emergence of the modulated symmetries upon gauging. We construct explicit lattice models in two and three spatial dimensions and develop complementary field-theoretic descriptions in arbitrary spatial dimensions that connect LSM anomaly inflow to higher-group symmetry structures governing the modulated symmetries. Our results provide a unified, nonperturbative framework that ties together LSM constraints and spatially modulated symmetries across dimensions.
Funding Information
  • Deutsche Forschungsgemeinschaft (277101999–TRR 183)
  • Deutsche Forschungsgemeinschaft (EXC 2004/1 - 390534769)
  • Japan Science and Technology Agency (JPMJCR24I3)
  • Villum Fonden (VIL60714)

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