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To analyze quantum many-body Hamiltonians, recently, machine learningtechniques have been shown to be quite useful and powerful. However, theapplicability of such machine learning solvers is still limited. Here, wepropose schemes that make it possible to apply machine learning techniques toanalyze fermion-boson coupled Hamiltonians and to calculate excited states. Asfor the extension to fermion-boson coupled systems, we study the Holstein modelas a representative of the fermion-boson coupled Hamiltonians. We show that themachine-learning solver achieves highly accurate ground-state energy, improvingthe accuracy substantially compared to that obtained by the variational MonteCarlo method. As for the calculations of excited states, we propose a differentapproach 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 twomethods using the one-dimensional $S=1/2$ Heisenberg chain. We also show thebenchmark for the frustrated two-dimensional $S=1/2$ $J_1$-$J_2$ Heisenbergmodel and show an excellent agreement with the results obtained by the exactdiagonalization. The extensions shown here open a way to analyze generalquantum many-body problems using machine learning techniques.

Machine Learning Quantum States -- Extensions to Fermion-Boson Coupled Systems and Excited-State Calculations