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

K. \c{C}evenM. \"O. OktelA. Kele\c{s}
Sep 2022
摘要
Quantum gas systems are ideal analog quantum simulation platforms fortackling some of the most challenging problems in strongly correlated quantummatter. However, they also expose the urgent need for new theoreticalframeworks. Simple models in one dimension, well studied with conventionalmethods, have received considerable recent attention as test cases for newapproaches. Ladder models provide the logical next step, where establishednumerical methods are still reliable, but complications of higher dimensionaleffects like gauge fields can be introduced. In this paper, we investigate theapplication of the recently developed neural-network quantum states in thetwo-leg Bose-Hubbard ladder under strong synthetic magnetic fields. Based onthe restricted Boltzmann machine and feedforward neural network, we show thatvariational neural networks can reliably predict the superfluid-Mott insulatorphase diagram in the strong coupling limit comparable with the accuracy of thedensity-matrix renormalization group. In the weak coupling limit, neuralnetworks also diagnose other many-body phenomena like the vortex, chiral andbiased-ladder phases. Our work demonstrates that the two-leg Bose-Hubbard modelwith magnetic flux is an ideal test ground for future developments ofneural-network quantum states.
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