  We investigate, by means of a field-theory analysis combined with the
density-matrix renormalization group (DMRG) method, a theoretical model for a
strongly correlated quantum system in one dimension realizing a
topologically-ordered Haldane phase ground state. The model consists of a
spin-1/2 Heisenberg chain coupled to a tight-binding chain via two competing
Kondo exchange couplings of different type: a "s-wave" Kondo coupling
($J^s_{K}$), and a less common "p-wave" ($J^p_{K}$) Kondo coupling. While the
first coupling is the standard Kondo interaction studied in many
condensed-matter systems, the latter has been recently introduced by Alexandrov
and Coleman [Phys. Rev. B 90, 115147 (2014)] as a possible mechanism leading to
a topological Kondo-insulating ground state in one dimension. As a result of
this competition, a topological quantum phase transition (TQPT) occurs in the
system for a critical value of the ratio $J^s_{K}/J^p_{K}$, separating a
(Haldane-type) topological phase from a topologically trivial ground state
where the system can be essentially described as a product of local singlets.
We study and characterize the TQPT by means for the magnetization profile, the
entanglement entropy and the full entanglement spectrum of the ground state.
Our results might be relevant to understand how topologically-ordered phases of
fermions emerge in strongly interacting quantum systems.
