Quantum many-fermion systems give rise to diverse states of matter that often reveal themselves in distinctive transport properties. While some of these states can be captured by microscopic models accessible to numerical exact quantum Monte Carlo simulations, it nevertheless remains challenging to numerically access their transport properties. Here, we demonstrate that quantum loop topography (QLT) can be used to directly probe transport by machine learning current-current correlations in imaginary time. We showcase this approach by studying the emergence of superconducting fluctuations in the negative-U Hubbard model and a spin-fermion model for a metallic quantum critical point. For both sign-free models, we find that the QLT approach detects a change in transport in very good agreement with their established phase diagrams. These proof-of-principle calculations combined with the numerical efficiency of the QLT approach point a way to identify hitherto elusive transport phenomena such as non-Fermi liquids using machine learning algorithms.
Bibliographical noteFunding Information:
Acknowledgements. We acknowledge useful discussions with Erez Berg, Yi-Ting Hsu, and Hong Yao. Y.Z. and E.-A.K. acknowledge the support from the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering under Award No. DE-SC0018946. The Cologne group acknowledges partial support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) Projektnummer 277101999–TRR 183 (Project No. B01). The numerical simulations were performed on the JUWELS cluster at FZ Jülich and the CHEOPS cluster at RRZK Cologne.
© 2019 American Physical Society.