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Optimally scrambling chiral spin-chain with effective black hole geometry
Aiden Daniel1, Andrew Hallam2, Matthew D Horner2,3
1School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, UK. py17ald@leeds.ac.uk.
Scientific Reports
|March 18, 2025
Summary
This study uses a chiral spin-chain to model black hole interiors, revealing chaotic dynamics and optimal scrambling behavior. The Lyapunov exponent increases linearly with temperature inside the black hole, unlike the quadratic increase outside.
Area of Science:
- Condensed matter physics
- Quantum gravity
- Black hole physics
Background:
- Significant interest exists in using condensed matter models to emulate black hole characteristics like Hawking radiation and scrambling.
- Chiral spin-chains offer a promising avenue for theoretical investigations into black hole physics.
Purpose of the Study:
- To investigate the chaotic dynamics and scrambling behavior within a chiral spin-chain model simulating a black hole interior.
- To analyze the temperature dependence of the Lyapunov exponent in different regions of the black hole model.
Main Methods:
- Utilized a chiral spin-chain model whose mean field theory mimics Dirac fermions in curved spacetime.
- Employed out-of-time-order correlations to diagnose many-body chaotic dynamics.
- Numerically computed the Lyapunov exponent within the simulated black hole interior and exterior regions.
Main Results:
- Observed strong correlations and many-body chaotic dynamics within the black hole interior region of the spin-chain.
- Found a linear increase in the Lyapunov exponent with temperature at low temperatures in the black hole interior, indicating optimal scrambling.
- Noted a contrasting quadratic temperature dependence of the Lyapunov exponent in the region outside the black hole.
Conclusions:
- The chiral spin-chain effectively models key black hole behaviors, including chaotic dynamics and optimal scrambling.
- The distinct temperature dependencies of the Lyapunov exponent provide insights into the differences between black hole interior and exterior dynamics.
- Findings contribute to understanding the connection between black hole geometry, quantum chaos, and quantum gravity principles.
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