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

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.

Source: arXiv:2603.19189v1 - http://arxiv.org/abs/2603.19189v1 PDF: https://arxiv.org/pdf/2603.19189v1 Original Link: http://arxiv.org/abs/2603.19189v1