Quantized topological invariant of symmetry-projected Gibbs states

2026/08/05 by Weiguang Cao, Haruki Watanabe
Physics and Astronomy · #cond-mat.str-el #cond-mat.other #cond-mat.stat-mech #hep-th

paper · pdf

6+16 pages, 2+2 figures, 1 table

arxiv created 2026/08/05 · arxiv updated 2026/08/06

Abstract

We study Gibbs states projected onto the symmetric sector of contractible one-form symmetries. In a three-dimensional cluster-model interpolation, this projection stabilizes symmetry-protected topological and projected-paramagnetic phases, both sharply distinct from thermal disorder. A flux-twisted membrane invariant distinguishes these three phases by the values -1,+1,0, respectively. These values are exact on the endpoint, self-dual, zero-temperature, and infinite-temperature lines; elsewhere their quantization requires positive spatial-sheet, winding-line, and interface tensions. Quantum Monte Carlo supports the quantization through tension diagnostics and direct finite-size estimates.

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