  We study three different measures of quantum correlations -- entanglement
spectrum, entanglement entropy, and logarithmic negativity -- for
(1+1)-dimensional massive scalar field in flat spacetime. The entanglement
spectrum for the discretized scalar field in the ground state indicates a
cross-over in the zero-mode regime, which is further substantiated by an
analytical treatment of both entanglement entropy and logarithmic negativity.
The exact nature of this cross-over depends on the boundary conditions used --
the leading order term switches from a $\log$ to $\log-\log$ behavior for the
Periodic and Neumann boundary conditions. In contrast, for Dirichlet, it is the
parameters within the leading $\log-\log$ term that are switched. We show that
this cross-over manifests as a change in the behavior of the leading order
divergent term for entanglement entropy and logarithmic negativity close to the
zero-mode limit. We thus show that the two regimes have fundamentally different
information content. Furthermore, an analysis of the ground state fidelity
shows us that the region between critical point $\Lambda=0$ and the crossover
point is dominated by zero-mode effects, featuring an explicit dependence on
the IR cutoff of the system. For the reduced state of a single oscillator, we
show that this cross-over occurs in the region $Nam_f\sim \mathscr{O}(1)$.
