  Topological phases exhibit a plethora of striking phenomena including
disorder-robust localization and propagation of waves of various nature. Of
special interest are the transitions between the different topological phases
which are typically controlled by the external parameters. In contrast, in this
Letter, we predict the topological transition in the two-particle interacting
system driven by the particles' quantum statistics. As a toy model, we
investigate an extended one-dimensional Hubbard model with two anyonic
excitations obeying fractional quantum statistics in-between bosons and
fermions. As we demonstrate, the interplay of two-particle interactions and
tunneling processes enables topological edge states of anyon pairs whose
existence and localization at one or another edge of the one-dimensional system
is governed by the quantum statistics of particles. Since a direct realization
of the proposed system is challenging, we develop a rigorous method to emulate
the eigenmodes and eigenenergies of anyon pairs with resonant electric
circuits.
