Authors
Jundi Wang, Yuxiao Chen, Huaqing Huang
Published in
Physical review letters. Volume 137. Issue 2. Pages 026401. Jul 10, 2026.
Abstract
Quantum geometry, characterized by the quantum metric and Berry curvature, is a powerful framework for understanding diverse physical phenomena in quantum materials, but its behavior in nonperiodic systems remains largely uncharted. Here, we uncover a universal mechanism for the divergent enhancement of the quantum metric in one-dimensional quasiperiodic systems, governed by the interplay of wave function criticality and spectral fractality. Using the paradigmatic Fibonacci chain, we demonstrate that the quantum metric displays a hierarchical scaling structure that mirrors the fractal organization of the energy spectrum. A real-space renormalization-group analysis yields an analytic power-law scaling, G∝(ΔE)^{-k}, between the quantum metric G and spectral gap ΔE, with the exponent k dictated by the system's self-similarity. This scaling persists in the critical Aubry-André-Harper model but disappears in both its localized and extended phases, confirming its universality across different quasiperiodic paradigms and its unique link to criticality. Our results show that the quantum metric provides a sensitive geometric indicator of quasiperiodic criticality, and highlight quasicrystals as promising platforms for realizing unconventional giant quantum geometric effects beyond the limits of periodic crystals.
PMID:
42503096
Bibliographic data and abstract were imported from PubMed on 26 Jul 2026.
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