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Quantum Chaos in Random Ising Networks

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2024

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Grabarits, András
Swain, Kasturi Ranjan
Chandarana, Pranav
Gómez-Ruiz, Fernando J.
Del Campo, Adolfo

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We report a systematic investigation of universal quantum chaotic signatures in the transverse field Ising model on an Erdős-Rényi network. This is achieved by studying local spectral measures such as the level spacing and the level velocity statistics. A spectral form factor analysis is also performed as a global measure, probing energy level correlations at arbitrary spectral distances. Our findings show that these measures capture the breakdown of chaotic behavior upon varying the connectivity and strength of the transverse field in various regimes. We demonstrate that the level spacing statistics and the spectral form factor signal this breakdown for sparsely and densely connected networks. The velocity statistics capture the surviving chaotic signatures in the sparse limit. However, these integrable-like regimes extend over a vanishingly small segment in the full range of connectivity.

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ISO 690GRABARITS, András, Kasturi Ranjan SWAIN, Mahsa SEYED HEYDARI, Pranav CHANDARANA, Fernando J. GÓMEZ-RUIZ, Adolfo DEL CAMPO, 2024. Quantum Chaos in Random Ising Networks
BibTex
@unpublished{Grabarits2024Quant-71492,
  year={2024},
  doi={10.48550/arXiv.2405.14376},
  title={Quantum Chaos in Random Ising Networks},
  author={Grabarits, András and Swain, Kasturi Ranjan and Seyed Heydari, Mahsa and Chandarana, Pranav and Gómez-Ruiz, Fernando J. and Del Campo, Adolfo}
}
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