Gauge invariant autoregressive neural network for quantum lattice models*

Gauge symmetries arise in various aspects of quantum mechanics, from condensed matter physics to high energy physics. We develop autoregressive neural networks that explicitly incorporate gauge symmetries and algebraic constraints and allow for efficient sampling. We analytically construct the gauge invariant neural network representation of the ground and excited states of the 2D and 3D toric codes, and the X-cube fracton model. We variationally optimize our neural networks to simulate the dynamics of the quantum link model of U(1) lattice gauge theory, determine the phase transition for the 2D Z₂ gauge theory, obtain the phase diagram and compute the central charge of the SU(2)₃ anyonic chain. Our approach provides a framework to construct neural networks with symmetries, and shows a powerful method for exploring condensed matter physics, high energy physics and quantum information science.