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arXiv · 2603.19189

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

Amogh Anakru·Linhao Li·Sarvesh Srinivasan·Zhen Bi
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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.

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Amogh Anakru, Linhao Li, Sarvesh Srinivasan, Zhen Bi. 2026-03-19. Matrix Product States for Modulated Symmetries: SPT, LSM, and Beyond. https://arxiv.org/abs/2603.19189

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