  Resolving the heavy fermion band in the conduction electron momentum resolved
spectral function of the Kondo lattice model is challenging since, in the weak
coupling limit, its spectral weight is exponentially small. In this article we
consider a composite fermion operator, consisting of a conduction electron
dressed by spin fluctuations that shares the same quantum numbers as the
electron operator. Using approximation free auxiliary field quantum Monte Carlo
simulations we show that for the SU(2) spin-symmetric model on the square
lattice at half filling, the composite fermion acts as a magnifying glass for
the heavy fermion band. In comparison to the conduction electron residue that
scales as $e^{-W/J_k}$ with $W$ the bandwidth and $J_k$ the Kondo coupling, the
residue of the composite fermion tracks $J_k$. This result holds down to $J_k/W
= 0.05$, and confirms the point of view that magnetic ordering, present below
$J_k/W = 0.18$, does not destroy the heavy quasiparticle. We furthermore
investigate the spectral function of the composite fermion in the ground state
and at finite temperatures, for SU($N$) generalizations of the Kondo lattice
model, as well as for ferromagnetic Kondo couplings, and compare our results to
analytical calculations in the limit of high temperatures, large-$N$,
large-$S$, and large $J_k$. Based on these calculations, we conjecture that the
composite fermion operator provides a unique tool to study the destruction of
the heavy fermion quasiparticle in Kondo breakdown transitions. The relation of
our results to scanning tunneling spectroscopy and photoemission experiments is
discussed.
