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

• URL: http://arxiv.org/abs/2603.19189v1
• Date: Thu, 19 Mar 2026 17:44:13 GMT
• Title: Matrix Product States for Modulated Symmetries: SPT, LSM, and Beyond
• Abstract summary: We show that the standard symmetry "push-through" condition for conventional global symmetry must be revised to account for symmetry modulation.<n>We classify one-dimensional SPT phases with modulated symmetries and formulate LSM-type constraints within the same MPS-based framework.
• Score: 4.85970118165132
• License: http://creativecommons.org/licenses/by/4.0/
• 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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