  The stability of the spin polaron quasiparticle, well established in studies
of a single hole in the 2D antiferromagnets, is investigated in the 1D
antiferromagnets using a t-J model. We perform an exact slave fermion
transformation to the holon-magnon basis, and diagonalize numerically the
resulting model in the presence of a single hole. We demonstrate that the spin
polaron collapses - and the spin-charge separation takes over - due to the
specific role played by the magnon-magnon interactions and the magnon hard-core
constraint in the 1D t-J model. Moreover, we prove that the spin polaron is
stable for any strength of the magnon-magnon interaction other than the unique
value found in a 1D antiferromagnet with the continuous symmetry of the spin
interactions. Fine-tuning to this unique value is extremely unlikely to occur
in quasi-1D antiferromagnets, therefore the spin polaron is the stable
quasiparticle of realistic 1D materials. Our results lead to a new
interpretation of the ARPES spectra of quasi-1D antiferromagnets in the spin
polaron language.
