Revealing quantum chaos with machine learning

Y. A. Kharkov, V. E. Sotskov, A. A. Karazeev, E. O. Kiktenko, A. K. Fedorov

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Understanding properties of quantum matter is an outstanding challenge in science. In this paper, we demonstrate how machine-learning methods can be successfully applied for the classification of various regimes in single-particle and many-body systems. We realize neural network algorithms that perform a classification between regular and chaotic behavior in quantum billiard models with remarkably high accuracy. We use the variational autoencoder for autosupervised classification of regular/chaotic wave functions, as well as demonstrating that autoencoders could be used as a tool for detection of anomalous quantum states, such as quantum scars. By taking this method further, we show that machine-learning techniques allow us to pin down the transition from integrability to many-body quantum chaos in Heisenberg XXZ spin chains. For both cases, we confirm the existence of universal W shapes that characterize the transition. Our results pave the way for exploring the power of machine-learning tools for revealing exotic phenomena in quantum many-body systems.

Original languageEnglish
Article number064406
Number of pages11
JournalPhysical Review B
Issue number6
Publication statusPublished - 2020

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    Kharkov, Y. A., Sotskov, V. E., Karazeev, A. A., Kiktenko, E. O., & Fedorov, A. K. (2020). Revealing quantum chaos with machine learning. Physical Review B, 101(6), [064406].