The fate of the spin polaron in the 1D antiferromagnets

<div> <div>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 <em>t-J</em> 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 <em>and</em> the magnon hard-core constraint in the 1D <em>t-J</em> 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 <em>quasi</em>-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 <em>quasi</em>-1D antiferromagnets in the spin polaron language.</div> </div>