Propagating S=1/2 particles in S=1 Haldane gap systems

TL;DR

This paper investigates the behavior of spin-1/2 particles in S=1 Haldane gap systems, analyzing their dispersion relations and interactions, inspired by recent experimental findings on related materials.

Contribution

It introduces a theoretical analysis of S=1/2 particle dispersion in S=1 Heisenberg and VBS models, considering small hopping amplitudes and impurity effects, extending understanding of edge states.

Findings

Identification of four-fold and two-fold degenerate bands due to impurity interactions

Analysis of the mixing between edge spins and impurity spins

Discussion of background-induced interactions among S=1/2 particles

Abstract

Inspired by the recent experiments on Y$_{2-x}$Ca$_x$BaNiO$_5$, (J. F. DiTusa {\it et al.}, Phys. Rev. Lett. 73, 1857 (1994)), we discuss the dispersion relation of the $s$=1/2 particles in the $s$=1 Heisenberg and VBS model in the limit of small hopping amplitudes. The effective $s$=1/2 edge spins mix with the spin of the impurity resulting in one four--fold and two two--fold degenarate bands. We briefly discuss the interaction between the $s$=1/2 particles arising from the background.