Exact representations of many body interactions with RBM neural networks

• URL: http://arxiv.org/abs/2005.03568v2
• Date: Fri, 8 Jan 2021 17:18:18 GMT
• Title: Exact representations of many body interactions with RBM neural networks
• Authors: Ermal Rrapaj, Alessandro Roggero
• Abstract summary: We exploit the representation power of RBMs to provide an exact decomposition of many-body contact interactions into one-body operators. This construction generalizes the well known Hirsch's transform used for the Hubbard model to more complicated theories such as Pionless EFT in nuclear physics.
• Score: 77.34726150561087
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Restricted Boltzmann Machines (RBM) are simple statistical models defined on a bipartite graph which have been successfully used in studying more complicated many-body systems, both classical and quantum. In this work, we exploit the representation power of RBMs to provide an exact decomposition of many-body contact interactions into one-body operators coupled to discrete auxiliary fields. This construction generalizes the well known Hirsch's transform used for the Hubbard model to more complicated theories such as Pionless EFT in nuclear physics, which we analyze in detail. We also discuss possible applications of our mapping for quantum annealing applications and conclude with some implications for RBM parameter optimization through machine learning.

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