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.
@article{arxiv.2603.19189,
title = {Matrix Product States for Modulated Symmetries: SPT, LSM, and Beyond},
author = {Amogh Anakru and Sarvesh Srinivasan and Linhao Li and Zhen Bi},
journal= {arXiv preprint arXiv:2603.19189},
year = {2026}
}