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<p>Higher-form symmetries acting on extended objects have reshaped our understanding of quantum phases and topological order, yet explicit incorporation of 1-form symmetry in tensor-network states remains unexplored. Here, we introduce a pull-through framework to embed 1-form symmetries into Projected Entangled-Pair States (PEPS), providing an operator-level definition of gauge flux and algebraic constraints on virtual symmetry matrices that encode anomalous braiding phases and enable efficient optimization of topologically ordered states. Our framework offers diagnostic tools for anomalies in topological phases and paves the way for more efficient tensor-network simulations in a variety of models with higher-form symmetries.</p>

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1-Form symmetric projected entangled-pair states

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年7月14日

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  • Yi Tan,
  • Wayne Zheng,
  • Ji-Yao Chen,
  • Didier Poilblanc,
  • Fei Ye,
  • Jia-Wei Mei

摘要

Higher-form symmetries acting on extended objects have reshaped our understanding of quantum phases and topological order, yet explicit incorporation of 1-form symmetry in tensor-network states remains unexplored. Here, we introduce a pull-through framework to embed 1-form symmetries into Projected Entangled-Pair States (PEPS), providing an operator-level definition of gauge flux and algebraic constraints on virtual symmetry matrices that encode anomalous braiding phases and enable efficient optimization of topologically ordered states. Our framework offers diagnostic tools for anomalies in topological phases and paves the way for more efficient tensor-network simulations in a variety of models with higher-form symmetries.