A framework maps Boltzmann-weighted lattice configurations to correlated random matrix ensembles via real-space to momentum-space variance profiles, deriving spectral moments and resolvent densities benchmarked on Ising and Edwards-Anderson models.
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Machine learning reconstruction accuracy is substantially higher for spectral-edge eigenstates than for mid-spectrum eigenstates, providing a new quantitative measure of information content in many-body quantum states.
Phase transitions are the points where vanishing parameter changes make two system states statistically distinguishable in the thermodynamic limit, identified via a distribution-free run test on the 2D Ising model.
The paper introduces neural-network trial wave functions for variational Monte Carlo, frames the variational method as unsupervised learning, and illustrates the approach on the Yukawa potential and hydrogen molecule.
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