  We study the ground state properties of bosons in a tilted double-well
system. We use fidelity susceptibility to identify the possible ground state
transitions under different tilt values. For a very small tilt (for example
$10^{-10}$), two transitions are found. For a moderate tilt (for example
$10^{-3}$), only one transition is found. For a large tilt (for example
$10^{-1}$), no transition is found. We explain this by analyzing the spectrum
of the ground state. The quantum discord and total correlation of the ground
state under different tilts are also calculated to indicate those transitions.
In the transition region, both quantities have peaks decaying exponentially
with particle number $N$. This means for a finite-size system the transition
region cannot be explained by the mean-field theory, but in the large-$N$ limit
it can be.
