Hofstadter's Butterfly Fractal from a Spin Network Perspective
Relating Hofstadter’s Butterfly to Spin Network Entanglement Spectra Hofstadter’s Butterfly is a fractal energy spectrum that emerges from quantum systems with periodic magnetic fields . Interestingly, spin networks also exhibit self-similarity and entanglement scaling , suggesting a deeper connection. Key Insights Hofstadter’s Butterfly is not just a fractal energy spectrum, but also exhibits fractal entanglement scaling. Entanglement entropy follows a self-similar structure , similar to spin networks in quantum gravity . This connects fractal quantum systems to entanglement-based holography , potentially linking quantum condensed matter physics to quantum gravity. The connection between quantum fractals and holography may provide new insights into quantum gravity.