  Light-matter interactions can be used as a tool to realize novel many-body
states of matter and to study the interplay between electronic and magnetic
degrees of freedom. In particular, tightly bound many-body states that behave
as coherent quasi-particles are rare, and may lead to unconventional
technological applications beyond the semi-conductor paradigm, particularly if
these excitations are bosonic and can condense. Two-dimensional magnetic
systems present a pristine platform to realize and study such states. We
construct a theory that explains the low-energy optical excitations at 1.476 eV
and 1.498 eV observed by photoluminiscence, optical absorption, and RIXS in the
van der Waals antiferromagnet NiPS$_3$. Using \textit{ab initio} methods, we
construct a two-band Hubbard model for two \textit{effective} Ni orbitals of
the original lattice. The dominant effective hopping corresponds to
third-nearest neighbours. This model exhibits two triplet-singlet excitations
of energy near two times the Hund exchange. From perturbation theory, we obtain
an effective model for the movement of the singlets in an antiferromagnetic
background, that we solve using a generalized self-consistent Born
approximation. These singlet excitations, dressed by a cloud of magnons, move
coherently as polaronic-like quasi-particles, "singlet polarons". Our theory
explains the main features of the observed spectra.
