To analyze quantum many-body Hamiltonians, recently, machine learning techniques have been shown to be quite useful and powerful. However, the applicability of such machine learning solvers is still limited. Here, we propose schemes that make it possible to apply machine learning techniques to analyze fermion-boson coupled Hamiltonians and to calculate excited states. As for the extension to fermion-boson coupled systems, we study the Holstein model as a representative of the fermion-boson coupled Hamiltonians. We show that the machine-learning solver achieves highly accurate ground-state energy, improving the accuracy substantially compared to that obtained by the variational Monte Carlo method. As for the calculations of excited states, we propose a different approach than that proposed in K. Choo et al., Phys. Rev. Lett. 121 (2018) 167204. We discuss the difference in detail and compare the accuracy of two methods using the one-dimensional $S=1/2$ Heisenberg chain. We also show the benchmark for the frustrated two-dimensional $S=1/2$ $J_1$ - $J_2$ Heisenberg model and show an excellent agreement with the results obtained by the exact diagonalization. The extensions shown here open a way to analyze general quantum many-body problems using machine learning techniques.To analyze quantum many-body Hamiltonians, recently, machine learning techniques have been shown to be quite useful and powerful. However, the applicability of such machine learning solvers is still limited. Here, we propose schemes that make it possible to apply machine learning techniques to analyze fermion-boson coupled Hamiltonians and to calculate excited states. As for the extension to fermion-boson coupled systems, we study the Holstein model as a representative of the fermion-boson coupled Hamiltonians. We show that the machine-learning solver achieves highly accurate ground-state energy, improving the accuracy substantially compared to that obtained by the variational Monte Carlo method. As for the calculations of excited states, we propose a different approach than that proposed in K. Choo et al., Phys. Rev. Lett. 121 (2018) 167204. We discuss the difference in detail and compare the accuracy of two methods using the one-dimensional $S=1/2$ Heisenberg chain. We also show the benchmark for the frustrated two-dimensional $S=1/2$ $J_1$-$J_2$ Heisenberg model and show an excellent agreement with the results obtained by the exact diagonalization. The extensions shown here open a way to analyze general quantum many-body problems using machine learning techniques.

arXiv:2001.02106Journal of the Physical Society of JapanApr 15, 202031 citations

Machine Learning for Quantum Many-body Problems

Yusuke Nomura

電子情報通信学会誌Nov 1, 20210 citations

Fast and Accurate Excitation Energies from Density Matrix Renormalization Group Calculations Improved by Machine Learning

Pavlo Golub, Libor Veis

An estimation of optoelectronic properties is a crucial necessity and an ongoing challenge in modern functional material science. This involves accurate accessing of ground and excited states in systems with complex electronic structure that are often too computationally expensive for accurate many-body methods. Building on our previous work on ground states [J. Phys. Chem. Lett. 2025, 16, 3295-3301], we present an efficient and cost-effective approach for evaluating electronic excitations in functional materials, combining the density matrix renormalization group method as a complete active space solver with machine learning techniques. We demonstrate its performance on π-electron-correlated systems, namely polycyclic aromatic compounds. The transferability and effectiveness of the derived machine learning model are demonstrated on a number of challenging examples with up to 34 π-electrons.An estimation of optoelectronic properties is a crucial necessity and an ongoing challenge in modern functional material science. This involves accurate accessing of ground and excited states in systems with complex electronic structure that are often too computationally expensive for accurate many-body methods. Building on our previous work on ground states [J. Phys. Chem. Lett. 2025, 16, 3295-3301], we present an efficient and cost-effective approach for evaluating electronic excitations in functional materials, combining the density matrix renormalization group method as a complete active space solver with machine learning techniques. We demonstrate its performance on π-electron-correlated systems, namely polycyclic aromatic compounds. The transferability and effectiveness of the derived machine learning model are demonstrated on a number of challenging examples with up to 34 π-electrons.

arXiv:2609.12616Sep 11, 20260 citations

S=1/2

Heisenberg chain. We also show the benchmark for the frustrated two-dimensional

S=1/2

J_1

J_2

Heisenberg model and show an excellent agreement with the results obtained by the exact diagonalization. The extensions shown here open a way to analyze general quantum many-body problems using machine learning techniques.