  Topological Kondo insulators are strongly correlated materials, where
itinerant electrons hybridize with localized spins giving rise to a
topologically non-trivial band structure. Here we use non-perturbative
bosonization and renormalization group techniques to study theoretically a
one-dimensional topological Kondo insulator. It is described as a
Kondo-Heisenberg model where the Heisenberg spin-1/2 chain is coupled to a
Hubbard chain through a Kondo exchange interaction in the p-wave channel - a
strongly correlated version of the prototypical Tamm-Shockley model. We derive
and solve renormalization group equations at two-loop order in the Kondo
parameter, and find that, at half-filling, the charge degrees of freedom in the
Hubbard chain acquire a Mott gap, even in the case of a non-interacting
conduction band (Hubbard parameter $U=0$). Furthermore, at low enough
temperatures, the system maps onto a spin-1/2 ladder with local ferromagnetic
interactions along the rungs, effectively locking the spin degrees of freedom
into a spin-$1$ chain with frozen charge degrees of freedom. This structure
behaves as a spin-1 Haldane chain, a prototypical interacting topological spin
model, and features two magnetic spin-$1/2$ end states for chains with open
boundary conditions. Our analysis allows to derive an insightful connection
between topological Kondo insulators in one spatial dimension and the
well-known physics of the Haldane chain, showing that the ground state of the
former is qualitatively different from the predictions of the naive mean-field
theory.
