Information-theoretic entropy imaging of quantum matter
Abstract
Phase transitions can generate intricate spatial organization invisible to spatially averaged probes, yet quantitative measures of this organization remain limited. Here we develop "entropy imaging," an information-theoretic technique that harnesses lossless compression to quantify spatial complexity, predictability, and order in quantum materials. Using this approach, emergent spatial textures can be imaged and converted into an experimentally-accessible observable: the computable information density (CID), a compression-based measure of information complexity that approaches the Shannon entropy rate in the large-system limit. Applied to millikelvin microwave impedance microscopy of graphene, the method reveals a pronounced maximum in the CID near quantum Hall transitions, a quantitative measure of the information-rich spatial organization of the critical landscape. A disordered Hofstadter model reproduces this behavior and shows that the CID can identify the quantum critical point from a sequence of images, without ensemble averaging over disorder realizations. The same framework tracks fractional quantum Hall transitions and resolves isolated fractional puddles that coexist with a disordered background. By contrast, the trivial band-edge crossover in a MoSe2/WS2 moiré heterobilayer exhibits qualitatively different behavior, suggesting that the pronounced CID enhancement observed at the quantum Hall critical point is not simply a generic feature of a conductive-insulating crossover. We further show that the geometric information encoded in CID is not reducible to a correlation length, and it can even distinguish spatial textures with identical multifractal statistics. Together, these results establish lossless compression as a framework for quantifying emergent spatial organization in quantum materials, with portability across imaging modalities and physical systems.
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BibTeX
@misc{wu2026informationtheoretic,
title = {{Information-theoretic entropy imaging of quantum matter}},
author = {Chen Wu and Leonard W. Cao and Lingyuan Lyu and Liam Cohen and Jiahui Nie and Can Uzundal and Yujia Hu and Quanjin Wang and Ziying Yan and Sneh Pancholi and Kenji Watanabe and Takashi Taniguchi and Feng Wang and Andrea F. Young and Tarun Grover and Monica T. Allen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35790},
eprint = {2610.35790},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35790},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Information-theoretic entropy imaging of quantum matter
AU - Chen Wu
AU - Leonard W. Cao
AU - Lingyuan Lyu
AU - Liam Cohen
AU - Jiahui Nie
AU - Can Uzundal
AU - Yujia Hu
AU - Quanjin Wang
AU - Ziying Yan
AU - Sneh Pancholi
AU - Kenji Watanabe
AU - Takashi Taniguchi
AU - Feng Wang
AU - Andrea F. Young
AU - Tarun Grover
AU - Monica T. Allen
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35790
UR - https://arxiv.org/abs/2610.35790
AB - Phase transitions can generate intricate spatial organization invisible to spatially averaged probes, yet quantitative measures of this organization remain limited. Here we develop "entropy imaging," an information-theoretic technique that harnesses lossless compression to quantify spatial complexity, predictability, and order in quantum materials. Using this approach, emergent spatial textures can be imaged and converted into an experimentally-accessible observable: the computable information density (CID), a compression-based measure of information complexity that approaches the Shannon entropy rate in the large-system limit. Applied to millikelvin microwave impedance microscopy of graphene, the method reveals a pronounced maximum in the CID near quantum Hall transitions, a quantitative measure of the information-rich spatial organization of the critical landscape. A disordered Hofstadter model reproduces this behavior and shows that the CID can identify the quantum critical point from a sequence of images, without ensemble averaging over disorder realizations. The same framework tracks fractional quantum Hall transitions and resolves isolated fractional puddles that coexist with a disordered background. By contrast, the trivial band-edge crossover in a MoSe2/WS2 moiré heterobilayer exhibits qualitatively different behavior, suggesting that the pronounced CID enhancement observed at the quantum Hall critical point is not simply a generic feature of a conductive-insulating crossover. We further show that the geometric information encoded in CID is not reducible to a correlation length, and it can even distinguish spatial textures with identical multifractal statistics. Together, these results establish lossless compression as a framework for quantifying emergent spatial organization in quantum materials, with portability across imaging modalities and physical systems.
ER -