  We predict that two correlated particles hopping on a one-dimensional Hubbard
lattice can show transient self-acceleration and self-induced Bloch
oscillations as a result of anti-Newtonian dynamics. Self-propulsion occurs for
two particles with opposite effective mass on the lattice and requires
long-range particle interaction. A photonic simulator of the two-particle
Hubbard model with controllable long-range interaction, where self-propulsion
can be observed, is discussed.
