Modulated symmetries from generalized Lieb-Schultz-Mattis anomalies

TL;DR

This paper develops a unified framework linking Lieb-Schultz-Mattis anomalies and spatially modulated symmetries across dimensions, using lattice models and field theories.

Contribution

It reveals how modulated symmetries and dipole algebras emerge from gauging symmetries with generalized LSM anomalies in higher dimensions.

Findings

Constructed explicit lattice models in 2D and 3D.

Connected LSM anomaly inflow to higher-group symmetries.

Provided a nonperturbative framework unifying LSM constraints and modulated symmetries.

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 one dimensional a spin chain, gauging procedures have linked modulated symmetry to LSM type anomaly, but a general understanding beyond 1D remains incomplete. We show that spatially modulated symmetries and their associated dipole algebras naturally emerge from gauging ordinary symmetries in the presence of generalized LSM type anomalies. 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.