Self-Similar Phase Diagram of the Fibonacci-Driven Quantum Ising Model
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1.
Freie Universität Berlin
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2.
California State University, Northridge
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3.
California Institute of Technology
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.
Copyright and License
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Acknowledgement
We thank Kang Yang for useful discussions. Research at Freie Universität Berlin was supported by Deutsche Forschungsgemeinschaft through CRC 183 as well as by the Einstein Research Unit on Quantum Devices. Work at CSUN and Caltech was supported by NSF PREP Grant No. PHY-2216774. G. R. is grateful for support through AFOSR MURI Grant No. FA9550-22-1-0339, as well as the Simons Foundation and the Institute of Quantum Information and Matter, an NSF Frontier Center. We thank the HPC service of ZEDAT, Freie Universität Berlin, for computing time [51].
Data Availability
The supporting data and codes for this article are available from Zenodo [52].
Supplemental Material
Technical details on Fibonacci words, single-particle evolution, fractal phase diagram, and effective Hamiltonians.
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Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2410.18219 (arXiv)
- Is supplemented by
- Dataset: 10.5281/zenodo.15065090 (DOI)
- Supplemental Material: https://journals.aps.org/prl/supplemental/10.1103/hn66-j8pt/supplement_PRLreresubmit.pdf (URL)
Funding
- Freie Universität Berlin
- Deutsche Forschungsgemeinschaft
- CRC 183
- National Science Foundation
- PHY-2216774
- United States Air Force Office of Scientific Research
- FA9550-22-1-0339
- Simons Foundation
- Institute of Quantum Information and Matter
Dates
- Accepted
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2025-06-09