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.

We kindly acknowledge support by the (Polish) National Science Centre (NCN, Poland) under Projects No. 2016/22/E/ST3/00560, 2016/23/B/ST3/00839, 2021/40/C/ST3/ 00177 as well as the Excellence Initiative of the University of Warsaw ('New Ideas' programme) IDUB program 501-D111-20-2004310 "Physics of the superconducting copper oxides: 'ordinary' quasiparticles or exotic partons?".Y.W. acknowledge support from the National Science Foundation (NSF) award DMR-2132338.M.B. acknowledges support from the Stewart Blusson Quantum Matter Institute and from NSERC. K.W. thanks the Stewart Blusson Quantum Matter Institute for the kind hospitality.This research was carried out with the support of the Interdisciplinary Center for Mathematical and Computational Modeling at the University of Warsaw (ICM UW) under grant no G73-29.