Machine learning quantum states — extensions to fermion–boson coupled systems and excited-state calculations

Yusuke Nomura

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

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 Choo et al., Phys. Rev. Lett. 121, 167204 (2018). 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 J1–J2 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.

Original languageEnglish
Article number054706
JournalJournal of the Physical Society of Japan
Volume89
Issue number5
DOIs
Publication statusPublished - 2020 May 15
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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