  Many-body localization (MBL) of a disordered interacting boson system in one
dimension is studied numerically at the filling faction one-half. The von
Neumann entanglement entropy SvN is commonly used to detect the MBL phase
transition but remains challenging to be directly measured. Based on the U(1)
symmetry from the particle number conservation, SvN can be decomposed into the
particle number entropy SN and the configuration entropy SC. In light of the
tendency that the eigenstate's SC nears zero in the localized phase, we
introduce a quantity describing the deviation of SN from the ideal
thermalization distribution; finite-size scaling analysis illustrates that it
shares the same phase transition point with SvN but displays the better
critical exponents. This observation hints that the phase transition to MBL
might largely be determined by SN and its fluctuations. Notably, the recent
experiments [A. Lukin et al., Science 364, 256 (2019); J. Leonard et al., Nat.
Phys. 19, 481 (2023)] demonstrated that this deviation can potentially be
measured through the SN measurement. Furthermore, our investigations reveal
that the thermalized states primarily occupy the low-energy section of the
spectrum, as indicated by measures of localization length, gap ratio, and
energy density distribution. This low-energy spectrum of the Bose model closely
resembles the entire spectrum of the Fermi (or spin XXZ) model, accommodating a
transition from the thermalized to the localized states. While, owing to the
bosonic statistics, the high-energy spectrum of the model allows the formation
of distinct clusters of bosons in the random potential background. We analyze
the resulting eigenstate properties and briefly summarize the associated
dynamics. To distinguish between the phase regions at the low and high
energies, a probing quantity based on the structure of SvN is also devised.
