Effective Hamiltonian description on monitored Majorana chains: correlated power-law hoppings and unconventional entanglement scaling

What the math gives to ML

The paper identifies a nonstandard mechanism in which correlated magnitudes of random long-range hoppings produce anomalous spectral-gap scaling and enhanced entanglement: the gap scales as \(\Delta(L)\sim L^{-z}\) with \(1<z<2\), while entropy is consistent with \([\ln L]^2\) rather than the usual \(\ln L\). The transferable asset is not merely long-range connectivity, but structured correlations between couplings across distances and locations. A neural-network analogue is a residual long-range mixer whose connection magnitudes are generated by a shared low-frequency latent field, then stabilized by explicit spectral normalization. This creates a testable multiscale architecture in which correlated weights should broaden scale coverage while preserving a measurable Jacobian stability boundary.