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  • Open Access

Phason-resolved finite-temperature topological diagnostics in quasiperiodic Chern-insulator approximants

Sheng Liu*, Wen-Yu Peng, and Chang-Wei Zou

Qi-Zhe Hou

  • *Contact author: shengliuver@gmail.com
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APS Open Sci. 1, 000182 – Published 23 October, 2026

DOI: https://doi.org/10.1103/4ssv-5mvp

Abstract

Finite-temperature topological diagnostics in quasiperiodic systems are subtle because quasiperiodicity removes the Bloch momentum torus on which mixed-state band indices are usually formulated. We study a quasiperiodic Qi-Wu-Zhang Chern insulator on finite Fibonacci approximants and use twisted boundary phases as an operational two-torus. A gap scan over L=21,34,55 shows that the fixed-boundary spectral gap can remain finite while extended low-gap regions appear elsewhere on the twist torus. Projected-Uhlmann diagnostics reveal a sharper finite-size result: The stability of the projected winding is not determined by the scalar minimum twist gap alone. A high-resolution L=34, 25×41 audit gives operational stability scales 5×10−4, 10−2, and 3×10−2 for three cases whose minimum twist gaps are all of order 10−3. The same ranking is obtained with projection bases on the θx=0 and exact θx=π slices. Direct phase-curve diagnostics show that collapse is associated with the loss or singularization of a 2π projected-Uhlmann phase winding, whereas stable cases preserve the winding despite small spectral gaps. Within the finite approximants studied here, these results identify phason-resolved boundary-phase geometry and projected-holonomy sensitivity, rather than the fixed-boundary gap or scalar minimum gap alone, as the mechanism controlling this finite-size projected diagnostic.

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APS Open Sci. 1, 000182– Published 23 October, 2026
Vol. 1
  • Received 28 June 2026
  • Revised 25 September 2026
  • Accepted 13 October 2026
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