We investigate the groundstate properties of a recently proposed model for a
topological Kondo insulator in one dimension (i.e., the p-wave
Kondo-Heisenberg lattice model) by means of the Density Matrix Renormalization
Group method. The non-standard Kondo interaction in this model is different
from the usual (i.e., local) Kondo interaction in that the localized spins
couple to the "p-wave" spin density of conduction electrons, inducing a
topologically non-trivial insulating groundstate. Based on the analysis of the
charge- and spin-excitation gaps, the string order parameter, and the spin
profile in the groundstate, we show that, at half-filling and low energies, the
system is in the Haldane phase and hosts topologically protected spin-1/2
end-states. Beyond its intrinsic interest as a useful "toy-model" to understand
the effects of strong correlations on topological insulators, we show that the
p-wave Kondo-Heisenberg model can be implemented in p−band optical lattices
loaded with ultra-cold Fermi gases.Comment: 8 pages, 4 figures, 1 appendi