Machine learning study of ground and photoexcited states in the half-filled one-dimensional extended Hubbard model

Aktuelle Probleme der Theoretischen Physik

Photoinduced nonequilibrium states can provide new insight into dynamical properties of strongly correlated electron systems. One of the typical and extensively studied systems is the half-filled one-dimensional extended Hubbard model (1DEHM). Here, we propose that the supervised machine learning (ML) can provide useful information for characterizing not only ground states but also photoexcited states in 1DEHM.  Constructing a neural network using entanglement spectra obtained by infinite-size density-matrix renormalization group, we confirm that bond-charge-density-wave (BCDW) phase remains stable in the thermodynamic limit [1]. Encouraged by the success of constructing a phase diagram of 1DEHM, we characterize photoexcited states by using the neural network trained for finite systems. Judging from the network, we find that a photon pulse induces a transition from the BCDW state to bond-spin-density-wave (BSDW) state [2]. We explicitly calculate the time evolution of order parameters and find that the order parameters of BSDW are indeed enhanced by photoexcitation as predicted by ML. Enhancement of the BSDW order in photoexcited states in 1DEHM has never been reported previously, despite extensive studies so far, thus demonstrating the advantage of ML to assist characterizing photoexcited quantum states.

[1] K. Shinjo, K. Sasaki, S. Hase, S. Sota, S. Ejima, S. Yunoki, and T. Tohyama, J. Phys. Soc. Jpn. 88, 065001 (2019).
[2] K. Shinjo, S. Sota, S. Yunoki, and T. Tohyama, arXiv:1901.07900.

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