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arXiv:1707.09723 · Journal of the Physical Society of Japan

Solving the Bose–Hubbard Model with Machine Learning

Hiroki Saito

Published Jul 31, 2017• 140 citations
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Abstract

Motivated by the recent successful application of artificial neural networks to quantum many-body problems [G. Carleo and M. Troyer, Science {\bf 355}, 602 (2017)], a method to calculate the ground state of the Bose-Hubbard model using a feedforward neural network is proposed. The results are in good agreement with those obtained by exact diagonalization and the Gutzwiller approximation. The method of neural-network quantum states is promising for solving quantum many-body problems of ultracold atoms in optical lattices.

DOI
10.7566/jpsj.86.093001

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Solving ground states of quantum many-body systems has been a long-standing problem in condensed matter physics. Here, we propose a new unsupervised machine learning algorithm to find the ground state of a general quantum many-body system utilizing the benefits of artificial neural network. Without assuming the specific forms of the eigenvectors, this algorithm can find the eigenvectors in an unbiased way with well controlled accuracy. As examples, we apply this algorithm to 1D Ising and Heisenberg models, where the results match very well with exact diagonalization.
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