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    Neural network impurity solver for real-frequency dynamical mean-field theory

    Fenglin Deng1,2, Yi Lu3,4, Xiaodong Cao1,2,*, and Zhicheng Zhong1,2

    • *Contact author: xdcao@ustc.edu.cn

    Phys. Rev. B 114, 165134 – Published 23 September, 2026

    DOI: https://doi.org/10.1103/3jm2-nqvn

    Abstract

    We introduce a neural network impurity solver for real-frequency dynamical mean-field theory that employs a multihead cross-attention mechanism to map hybridization functions to spectral functions, conditioned on impurity parameters. Trained on high-quality matrix product states data from complex contour time evolution and incorporating derivative constraints with respect to the complex-time angle, our model achieves smooth generalization to the real-frequency axis. Benchmarking on the single-band Hubbard model for the Bethe lattice demonstrates quantitative accuracy across metallic, strongly correlated, and insulating regimes.

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