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Matrix Product States for Modulated Symmetries: SPT, LSM, and Beyond

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arxiv 2603.19189 v2 pith:75PH2SWG submitted 2026-03-19 cond-mat.str-el quant-ph

Matrix Product States for Modulated Symmetries: SPT, LSM, and Beyond

Amogh Anakru , Linhao Li , Sarvesh Srinivasan , Zhen Bi This is my paper
classification cond-mat.str-el quant-ph
keywords modulatedsymmetriessymmetryconditionconstraintsframeworkgeneralizedmatrix
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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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Translationally Covariant Modulated Symmetries: Classification and Goldstone

    cond-mat.str-el 2026-06 unverdicted novelty 7.0

    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.

  2. Matrix Product States for Modulated Topological Phases: Crystalline Equivalence Principle and Lieb-Schultz-Mattis Constraints

    cond-mat.str-el 2026-03 unverdicted novelty 7.0

    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.

  3. Projector, Neural, and Tensor-Network Representations of $\mathbb{Z}_N$ Cluster and Dipolar-cluster SPT States

    cond-mat.dis-nn 2026-04 unverdicted novelty 6.0

    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.

  4. Lieb-Schultz-Mattis Anomalies and Anomaly Matching

    cond-mat.str-el 2026-04 unverdicted novelty 2.0

    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.