  Fermion-exciton condensation in which both fermion-pair (i.e.,
superconductivity) and exciton condensations occur simultaneously in a single
coherent quantum state has recently been conjectured to exist. Here, we capture
the fermion-exciton condensation through a model Hamiltonian that can recreate
the physics of this new class of highly correlated condensation phenomena. We
demonstrate that the Hamiltonian generates the large-eigenvalue signatures of
fermion-pair and exciton condensations for a series of states with increasing
particle numbers. The results confirm that the dual-condensate wave function
arises from the entanglement of fermion-pair and exciton wave functions, which
we previously predicted in the thermodynamic limit. This model Hamiltonian --
generalizing well-known model Hamiltonians for either superconductivity or
exciton condensation -- can explore a wide variety of condensation behavior. It
provides significant insights into the required forces for generating a
fermion-exciton condensate, which will likely be invaluable for realizing such
condensations in realistic materials with applications from superconductors to
excitonic materials.
