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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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.
Low-energy eigenstates of a spin chain allow a neural network to reconstruct the Hamiltonian accurately, while mid-spectrum eigenstates do not, defining a spectral 'learnability' gap.
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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Random Matrix Spectra from Boltzmann-Weighted Lattice Ensembles
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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Phase Transitions as the Breakdown of Statistical Indistinguishability
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.
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Information in Many-body Eigenstates: A Question of Learnability
Low-energy eigenstates of a spin chain allow a neural network to reconstruct the Hamiltonian accurately, while mid-spectrum eigenstates do not, defining a spectral 'learnability' gap.
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Introduction to the artificial neural network-based variational Monte Carlo method
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.