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Self-Similar Phase Diagram of the Fibonacci-Driven Quantum Ising Model
Harald Schmid1, Yang Peng2, Gil Refael3
1Freie Universität Berlin, Dahlem Center for Complex Quantum Systems and Fachbereich Physik, 14195 Berlin, Germany.
Physical Review Letters
|July 31, 2025
Summary
Researchers explored a quantum Ising model with Fibonacci dynamics, discovering self-similar phase diagram regions hosting Majorana zero modes (MZM) and Majorana golden-ratio modes (MGM). These findings are testable on quantum information processors.
Area of Science:
- Condensed Matter Physics
- Quantum Information Science
- Mathematical Physics
Background:
- The quantum Ising model is a fundamental model in condensed matter physics.
- Fibonacci dynamics introduce unique temporal evolution patterns.
- Majorana zero modes (MZM) are exotic quasiparticles with potential applications in topological quantum computing.
Purpose of the Study:
- To investigate the phase diagram of a stroboscopic quantum Ising model with Fibonacci dynamics.
- To identify regions exhibiting Majorana zero modes (MZM) and Majorana golden-ratio modes (MGM).
- To understand the self-similar evolution of these regions and the impact of perturbations.
Main Methods:
- Analysis of boundary spin correlation functions in finite-length spin chains.
- Utilizing stroboscopic quantum dynamics with Fibonacci sequences.
- Identifying self-similarity transforms governing phase diagram evolution.
Main Results:
- Identified distinct regions in the phase diagram hosting both MZM and MGM.
- Observed self-similar evolution of these regions with increasing simulation time.
- Characterized the governing self-similarity transform.
- Demonstrated that integrability-breaking perturbations cause temporal decay of correlations, limiting self-similarity.
Conclusions:
- The stroboscopic quantum Ising model with Fibonacci dynamics exhibits predictable, self-similar phase diagrams.
- Majorana modes and their golden-ratio counterparts appear in specific, evolving regions.
- The findings provide testable predictions for current quantum information processors.
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