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Fluctuation based interpretable analysis scheme for quantum many-body snapshots
by Henning Schloemer, Annabelle Bohrdt
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Microscopically understanding and classifying phases of matter is at the heart of strongly-correlated quantum physics. With quantum simulations, genuine projective measurements (snapshots) of the many-body state can be taken, which include the full information of correlations in the system. The rise of deep neural networks has made it possible to routinely solve abstract processing and classification tasks of large datasets, which can act as a guiding hand for quantum data analysis. However, though proven to be successful in differentiating between different phases of matter, conventional neural networks mostly lack interpretability on a physical footing. Here, we combine confusion learning with correlation convolutional neural networks, which yields fully interpretable phase detection in terms of correlation functions. In particular, we study thermodynamic properties of the 2D Heisenberg model, whereby the trained network is shown to pick up qualitative changes in the snapshots above and below a characteristic temperature where magnetic correlations become significantly long-range. We identify the full counting statistics of nearest neighbor spin correlations as the most important quantity for the decision process of the neural network, which go beyond averages of local observables. With access to the fluctuations of second-order correlations -- which indirectly include contributions from higher order, long-range correlations -- the network is able to detect changes of the specific heat and spin susceptibility, the latter being in analogy to magnetic properties of the pseudogap phase in high-temperature superconductors. By combining the confusion learning scheme with transformer neural networks, our work opens new directions in interpretable quantum image processing being sensible to long-range order.
Published as SciPost Phys. 15, 099 (2023)
Submission & Refereeing History
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- Report 4 submitted on 2023-05-19 23:57 by Anonymous
- Report 3 submitted on 2023-05-19 09:59 by Prof. van Nieuwenburg
- Report 2 submitted on 2023-05-16 17:54 by Anonymous
- Report 1 submitted on 2023-05-09 12:23 by Anonymous
Reports on this Submission
Report 1 by Everard van Nieuwenburg on 2023-7-6 (Invited Report)
This revised version of the manuscript is a clear improvement over v1, in my opinion. The message of the paper is more pronounced, and previously stated but unmotivated parts of the text now have proper context.
I remain positive in my assessment. Especially taken together with the other reports on v1, and the authors' implementation of that feedback, I have no further requested changes.