Information in Many-body Eigenstates: A Question of Learnability

Abstract:To what extent do individual eigenstates encode information about their parent Hamiltonian, and how does this encoding vary across the spectrum? We introduce \emph{learnability} as a new framework to quantify this information, measured by the precision with which a machine learning model can reconstruct a Hamiltonian from a limited set of eigenstates. For many-body quantum systems, there is a contrast between the eigenstates near the spectral edges (low-entanglement, highly-structured states) and those far from the spectral edges (high-entanglement, near-random states). Using an encoder-decoder neural network for a non-integrable spin chain, we show that this dichotomy results in a stark difference in learnability: spectral-edge eigenstates allow for higher-accuracy Hamiltonian reconstruction using significantly fewer eigenstates, compared to mid-spectrum eigenstates. Our results provide a new lens through which to view the spectral structure of many-body systems.

Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn)

arXiv:2605.03043 [quant-ph]

(or arXiv:2605.03043v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2605.03043 Focus to learn more arXiv-issued DOI via DataCite

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