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

TL;DR

This paper demonstrates how a simple neural network can uncover sign rules in qubit lattice models, linking neural network outputs to classical physical quantities and analyzing quantum fluctuation effects.

Contribution

It introduces a shallow neural network approach to reveal sign rules in various qubit lattice models, connecting neural outputs to classical physical parameters.

Findings

Neural network visualizes sign rules as classical quantities like pitch angles.

Quantum fluctuations cause deviations from ideal sign rule accuracy.

Method applies across multiple models including Ising, XY, Heisenberg, and Fermi-Hubbard.

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.