Topology of many-body edge and extended quantum states in an open spin chain: 1/3--plateau, Kosterlitz-Thouless transition, and Luttinger liquid

Quantum many-body edge and extended magnon excitations from the 1/3 – plateau of the anisotropic Heisenberg model on an open AB${}_2$ chain in a magnetic field $h$ are unveiled using the density matrix renormalization group and exact diagonalization. By tuning both the anisotropy and $h$ in the rich phase diagram, the edge states penetrate in the bulk, whose gap closes in a symmetry-protected topological Kosterlitz-Thouless transition. Also, we witness the squeezed chain effect, the breaking of the edge states degeneracy, and a topological change of the excitations from gapped magnons with quadratic long-wavelength dispersion to a linear spinon dispersion in the Luttinger liquid gapless phase as the anisotropy $\lambda$ approaches the critical point from the $\lambda >0$ side of the phase diagram.