Neural-network quantum states in optical lattice with artificial magnetic flux

Recently, few-leg ladder Hubbard models received considerable theoretical and experimental interest since they can be studied with established numerical methods, and complications of higher dimensional effects like gauge fields can be introduced optically in cold atom experiments. In this talk, we demonstrate the application of neural-network quantum states in the two-leg Bose-Hubbard ladder under strong synthetic magnetic fields using the restricted Boltzmann machine and feedforward neural networks. We show that variational neural networks can reliably predict the superfluid-Mott insulator transition in the strong coupling limit comparable with the accuracy of the density-matrix renormalization group. In the weak coupling limit, neural networks also diagnose other many-body phenomena like the vortex, chiral and biased-ladder phases. We will also present applications of neural-networks in finite two-dimensional systems with artificial magnetic fields.