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arXiv · 2302.02523

Principle of learning sign rules by neural networks in qubit lattice models

Jin Cao·Shijie Hu·Zhiping Yin·Ke Xia
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Abstract

A neural network is a powerful tool that can uncover hidden laws beyond human intuition. However, it often appears as a black box due to its complicated nonlinear structures. By drawing upon the Gutzwiller mean-field theory, we can showcase a principle of sign rules for ordered states in qubit lattice models. We introduce a shallow feed-forward neural network with a single hidden neuron to present these sign rules. We conduct systematical benchmarks in various models, including the generalized Ising, spin-$1/2$ XY, (frustrated) Heisenberg rings, triangular XY antiferromagnet on a torus, and the Fermi-Hubbard ring at an arbitrary filling. These benchmarks show that all the leading-order sign rule characteristics can be visualized in classical forms, such as pitch angles. Besides, quantum fluctuations can result in an imperfect accuracy rate quantitatively.

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Jin Cao, Shijie Hu, Zhiping Yin, Ke Xia. 2023-02-06. Principle of learning sign rules by neural networks in qubit lattice models. https://doi.org/10.1103/physrevb.108.195127

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