  We present a minimal non-Hermitian model where a topologically nontrivial
complex energy spectrum is induced by inter-particle interactions. Our model
consists of a one-dimensional chain with a dynamical non-Hermitian gauge field
with density dependence. The model is topologically trivial for a single
particle system, but exhibits nontrivial non-Hermitian topology with a point
gap when two or more particles are present in the system. We construct an
effective doublon model to describe the nontrivial topology in the presence of
two particles, which quantitatively agrees with the full interacting model. Our
model can be realized by modulating hoppings of the Hatano-Nelson model; we
provide a concrete Floquet protocol to realize the model in atomic and optical
settings.
