Matrix Product States for Modulated Symmetries: SPT, LSM, and Beyond
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917353658253312 |
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| author | Anakru, Amogh Srinivasan, Sarvesh Li, Linhao Bi, Zhen |
| author_facet | Anakru, Amogh Srinivasan, Sarvesh Li, Linhao Bi, Zhen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19189 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Matrix Product States for Modulated Symmetries: SPT, LSM, and Beyond Anakru, Amogh Srinivasan, Sarvesh Li, Linhao Bi, Zhen Strongly Correlated Electrons Quantum Physics 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. |
| title | Matrix Product States for Modulated Symmetries: SPT, LSM, and Beyond |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2603.19189 |