Motion of Bound Domain Walls in a Spin Ladder

TL;DR

This paper investigates the behavior of bound domain wall pairs in spin ladder models with Ising-like interactions, revealing their dynamics and spectral features, and connecting findings to experimental observations.

Contribution

It introduces a perturbative approach to study bound spinon pairs in spin ladders with Ising-like interactions, highlighting their delocalization and propagation mechanisms.

Findings

Bound spinon pairs are coupled in the models studied.

Delocalization of bound pairs occurs due to ring exchange interactions.

The dynamic structure factor shows an almost symmetric lineshape.

Abstract

The elementary excitation spectrum of the spin-$\frac{1}{2}$ antiferromagnetic (AFM) Heisenberg chain is described in terms of a pair of freely propagating spinons. In the case of the Ising-like Heisenberg Hamiltonian spinons can be interpreted as domain walls (DWs) separating degenerate ground states. In dimension $d>1$, the issue of spinons as elementary excitations is still unsettled. In this paper, we study two spin-$\frac{1}{2}$ AFM ladder models in which the individual chains are described by the Ising-like Heisenberg Hamiltonian. The rung exchange interactions are assumed to be pure Ising-type in one case and Ising-like Heisenberg in the other. Using the low-energy effective Hamiltonian approach in a perturbative formulation, we show that the spinons are coupled in bound pairs. In the first model, the bound pairs are delocalized due to a four-spin ring exchange term in the effective Hamiltonian. The appropriate dynamic structure factor is calculated and the associated lineshape is found to be almost symmetric in contrast to the 1d case. In the case of the second model, the bound pair of spinons lowers its kinetic energy by propagating between chains. The results obtained are consistent with recent theoretical studies and experimental observations on ladder-like materials.