Neural-network quantum states for a two-leg Bose-Hubbard ladder under magnetic flux

Quantum gas systems are ideal analog quantum simulation platforms for tackling some of the most challenging problems in strongly correlated matter. However, they also expose urgent need new theoretical frameworks. Simple models one dimension, well studied with conventional methods, have received considerable recent attention as test cases approaches. Ladder provide logical next step, where established numerical methods still reliable, but complications higher dimensional effects like gauge fields can be introduced. In this paper, we investigate application recently developed neural-network states two-leg Bose-Hubbard ladder under strong synthetic magnetic fields. Based on restricted Boltzmann machine and feedforward neural network, show that variational networks reliably predict superfluid-Mott insulator phase diagram coupling limit comparable accuracy density-matrix renormalization group. weak limit, diagnose other many-body phenomena such vortex, chiral, biased-ladder phases. Our work demonstrates model flux is an ground future developments states.