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.

Location: Tewksbury, MA, USA

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