Magnon Wave-function and Impurity Effects in S=1 Antiferromagnetic Chains: A Large-n Approach

TL;DR

This paper develops a large-n approximation to analyze magnon wave-functions and impurity effects in S=1 antiferromagnetic chains, revealing boundstate conditions and energy behaviors near the Haldane gap.

Contribution

It introduces a large-n theoretical approach to study impurity effects and magnon boundstates in S=1 chains, extending understanding of their excitation spectrum.

Findings

Magnon boundstates exist below the Haldane gap for small negative J'-J.

Binding energy vanishes quadratically as J approaches J' from below.

Boundstate existence depends on a critical positive J'-J value.

Abstract

A large-n approximation to the S=1 antiferromagnetic chain, using the symmetric tensor representation and its conjugate, is developed to order 1/n in order to calculate the magnon wave-function and to study the effect of modifying the exchange coupling from J to J' on a single link. It is shown that a magnon boundstate exists below the Haldane gap for arbitrarily small negative J'-J but only above a certain critical value of J'-J for positive values. In the former case the binding energy vanishes as the square of (J-J').