  Inspired by the recent development of an algebraic model which provides an
adequate and unified description of the internal structure of the lowest-lying
pseudo-scalar mesons, belonging both to the light quarks sector and to the one
of heavy quarks, we perform its first extension to the vector-meson case. The
algebraic model describes meson's structure in terms of the spectral density
function that appears in a Nakanishi integral representation of the covariant
quark-antiquark bound-state amplitude, \emph{i.e.}, the Bethe-Salpeter
amplitude. We compute the leading-twist light-front wave functions of the
$\rho(770)$, $\phi(1020)$, $J/\psi$ and $\Upsilon(1S)$ mesons through their
connection with the parton distribution amplitudes. Among the results we
present, the following are of particular interest: (i) transverse light-front
wave functions can be obtained algebraically from the corresponding parton
distribution amplitudes, whereas that is not the case for longitudinal
light-front wave functions, which requires an intermediate step where a
spectral density function must be derived from the particular parton
distribution amplitude; (ii) the derived spectral density functions show marked
differences between light and heavy vector mesons, the latter being narrower as
compared to the former; these are also non-positive definite, although the
integral over the entire curve is larger than zero as expected; and (iii) the
longitudinal and transverse light-front wave functions of vector mesons with
light quark content exhibit steep $x$- and $p_\perp^2$-dependence, while those
of the $J/\psi$ and $\Upsilon(1S)$ mesons are characterized by narrow
distributions in the $x$-range but, comparatively, much more gradual fall-offs
with respect to the $p_\perp^2$-range depicted.
