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A nearest-neighbor, frustration-free spin \(\frac{1}{2}\) chain can be constructed via projectors of various ranks á la Bravyi-Gosset. We show that in the rank 1 case this system is gapped and has two ground states resembling ferromagnetic states. These states spontaneously break the non-invertible symmetry connecting them. The latter is proved using the machinery of algebraic quantum theory. The non-invertible symmetries of this system do not come from a duality.

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Non-invertible Symmetry Breaking in a Frustration-Free Spin Chain

  • 会议论文

  • 发表日期：

    2025年

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  • Akash Sinha,
  • Vivek Kumar Singh,
  • Pramod Padmanabhan,
  • Kun Hao,
  • Vladimir Korepin

摘要

A nearest-neighbor, frustration-free spin \(\frac{1}{2}\) chain can be constructed via projectors of various ranks á la Bravyi-Gosset. We show that in the rank 1 case this system is gapped and has two ground states resembling ferromagnetic states. These states spontaneously break the non-invertible symmetry connecting them. The latter is proved using the machinery of algebraic quantum theory. The non-invertible symmetries of this system do not come from a duality.