  While neutrino oscillations have led to attention and research on field
mixing arising from quadratic interactions, the field mixing inherent in
clothed particles is more fundamental, serving as a significant source of
complexity and non-perturbative challenges in quantum field theory. We present
an example of an analytical solution for field mixing involving a three-point
interaction between a bosonic field and a fermionic field. Specifically, we
study the Rothe-Stamatescu (RS) model and utilize lattice regularization to
provide a well-defined Hamiltonian which is absent in the original continuous
RS model. Due to the complexity introduced by three-point interactions compared
to quadratic interactions, the Fock representation commonly used in discussions
of field mixing does not work well; instead, we define a representation based
on real space to investigate the physical vacuum and clothed particles. These
eigenstates not only reveal the field mixing between the bosonic and fermionic
fields but also allow us to directly observe the spatial entanglement
structure.
