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Self-Similar Phase Diagram of the Fibonacci-Driven Quantum Ising Model

Harald Schmid1, Yang Peng2, Gil Refael3, and Felix von Oppen1

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Phys. Rev. Lett. 134, 240404 – Published 20 June, 2025

DOI: https://doi.org/10.1103/hn66-j8pt

Abstract

We study a stroboscopic quantum Ising model with Fibonacci dynamics. We use its boundary spin correlation functions in long but finite chains to identify regions in the phase diagram which exhibit Majorana zero modes (MZM) as well as Majorana golden-ratio modes (MGM). We find that these regions evolve in a self-similar manner with increasing simulation time and identify the self-similarity transform which governs this evolution of the phase diagram. Integrability-breaking perturbations lead to a temporal decay of the boundary spin correlations, ultimately limiting the self-similarity of the phase diagram. Our predictions are testable with current quantum information processors.

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Phys. Rev. Lett. 134, 240404– Published 20 June, 2025
  • Received 2 November 2024
  • Revised 24 March 2025
  • Accepted 9 June 2025
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