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

TL;DR

This paper investigates the topological and many-body properties of edge and bulk excitations in an open anisotropic Heisenberg spin chain, revealing phase transitions, topological changes, and the emergence of Luttinger liquid behavior through numerical methods.

Contribution

It uncovers the interplay of topology, edge states, and phase transitions in an open spin chain, highlighting the transition from gapped magnons to a Luttinger liquid with linear spinon dispersion.

Findings

Edge states penetrate the bulk as the gap closes at the transition.

A Kosterlitz-Thouless transition protects the topological phase.

Transition from quadratic magnon to linear spinon dispersion in the gapless phase.

Abstract

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.