Reflection positivity and a refined index for 2d invertible phases

• URL: http://arxiv.org/abs/2509.01711v1
• Date: Mon, 01 Sep 2025 18:46:41 GMT
• Title: Reflection positivity and a refined index for 2d invertible phases
• Authors: Nikita Sopenko,
• Abstract summary: We provide a mathematical model in which every 2d invertible state admits a reflection-positive representative.<n>We prove that reflection positivity provides a canonical lift from the set of invertible phases to the set of invertible phases protected by a $mathbbZ/N$-rotational symmetry.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We analyze the validity of reflection positivity in the classification of invertible phases of quantum spin systems. We provide a mathematical model in which every 2d invertible state admits a reflection-positive representative. We prove that reflection positivity provides a canonical lift from the set of invertible phases to the set of invertible phases protected by a $\mathbb{Z}/N$-rotational symmetry. Using this, we define a refined version of the index recently introduced by the author. This refined version conjecturally provides a microscopic characterization of an invariant that coincides with the chiral central charge $c_-$ when conformal field theory effectively describes the boundary modes.

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