The paper classifies one-dimensional Abelian translationally covariant modulated symmetries via Jordan normal forms and derives their Goldstone actions, which modify the conventional theorem by type of symmetry.
Matrix Product States for Modulated Symmetries: SPT, LSM, and Beyond
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Matrix product states (MPS) provide a powerful framework for characterizing one-dimensional symmetry-protected topological (SPT) phases of matter and for formulating Lieb-Schultz-Mattis (LSM)-type constraints. Here we generalize the MPS formalism to translationally invariant systems with general modulated symmetries. We show that the standard symmetry "push-through" condition for conventional global symmetry must be revised to account for symmetry modulation, and we derive the appropriate generalized condition. Using this generalized push-through structure, we classify one-dimensional SPT phases with modulated symmetries and formulate LSM-type constraints within the same MPS-based framework.
years
2026 4verdicts
UNVERDICTED 4representative citing papers
Modulated SPT phases in 1D are classified by H²(G, U(1)_s) and obey LSM-type theorems forbidding symmetric short-range entangled ground states.
Z_N cluster and dipolar-cluster SPT wavefunctions admit closed-form projector, neural, and tensor-product representations that generalize Z_2 constructions and yield a TPS benchmarked against MPS via DMRG.
The review summarizes Lieb-Schultz-Mattis anomalies and anomaly matching, starting from spin chains and extending to higher dimensions, disordered systems, fermionic systems, and symmetry-protected topological phases.
citing papers explorer
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Translationally Covariant Modulated Symmetries: Classification and Goldstone
The paper classifies one-dimensional Abelian translationally covariant modulated symmetries via Jordan normal forms and derives their Goldstone actions, which modify the conventional theorem by type of symmetry.
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Matrix Product States for Modulated Topological Phases: Crystalline Equivalence Principle and Lieb-Schultz-Mattis Constraints
Modulated SPT phases in 1D are classified by H²(G, U(1)_s) and obey LSM-type theorems forbidding symmetric short-range entangled ground states.
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Projector, Neural, and Tensor-Network Representations of $\mathbb{Z}_N$ Cluster and Dipolar-cluster SPT States
Z_N cluster and dipolar-cluster SPT wavefunctions admit closed-form projector, neural, and tensor-product representations that generalize Z_2 constructions and yield a TPS benchmarked against MPS via DMRG.
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Lieb-Schultz-Mattis Anomalies and Anomaly Matching
The review summarizes Lieb-Schultz-Mattis anomalies and anomaly matching, starting from spin chains and extending to higher dimensions, disordered systems, fermionic systems, and symmetry-protected topological phases.