  Using the multiphase transport (AMPT) model, we study the relative neutron
density fluctuation and neutron-proton correlation in matter produced by Au+Au
collisions at $\sqrt{s_\text{NN}} = $7.7-200 GeV. The rapidity, centrality, and
energy dependence of these two observations are also discussed. The light
nuclei yield ratio of proton, deuteron, and triton $N_tN_p/N_d^2$ calculated
directly from the relative neutron density fluctuation and neutron-proton
correlation, decreases with rapidity coverage and increases with collision
centrality. Our study also found that the ratio does not exhibit any
non-monotonic behavior in collision energy dependence. Since there is no
first-order phase transition or critical physics in the AMPT model, our work
provides a reference for extracting the relative neutron density fluctuation
from light nuclei production in experiments.
