Quantum chaos in random Ising networks

We report a systematic investigation of universal quantum chaotic signatures in the transverse field Ising model on an Erdos-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 the strength of the transverse field in various regimes. We demonstrate that the level spacing distribution 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 integrablelike regimes extend over a vanishingly small segment in the full range of connectivity. Our work elucidates the emergence of quantum chaos in relation to network topology, establishing a bridge between many-body physics and network theory.