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      Self-learning Monte Carlo method with Behler-Parrinello neural networks

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          Abstract

          Self-learning Monte Carlo method (SLMC) is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. Its applications are, however, limited. This is because it is not obvious to find the explicit form of the effective Hamiltonians. Particularly, it is difficult to make effective Hamiltonians including many body interactions. In order to overcome this critical difficulty, we introduce the Behler-Parrinello neural networks (BPNNs) as ``effective Hamiltonian'' without any prior knowledge, which is used to construct the potential-energy surfaces in interacting many particle systems for molecular dynamics. We construct self-learning continuous-time interaction-expansion quantum Monte Carlo method with BPNNs and apply it to quantum impurity models. We observed significant improvement of the acceptance ratio from 0.01 (the effective Hamiltonian with the explicit form) to 0.76 (BPNN). This drastic improvement implies that the BPNN effective Hamiltonian includes many body interaction, which is omitted in the effective Hamiltonian with the explicit forms. The BPNNs make SLMC more promising.

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          Numerical study of the two-dimensional Hubbard model

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            Two-dimensional Hubbard model: Numerical simulation study

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              Learning phase transitions by confusion

              A neural-network technique can exploit the power of machine learning to mine the exponentially large data sets characterizing the state space of condensed-matter systems. Topological transitions and many-body localization are first on the list.
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                Author and article information

                Journal
                13 July 2018
                Article
                1807.04955
                65179e9b-2577-4138-ab9c-abd026437072

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                6 pages, 3 figures + 1 page supplemental materials
                cond-mat.str-el physics.comp-ph

                Condensed matter,Mathematical & Computational physics
                Condensed matter, Mathematical & Computational physics

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