The Haldane Energy Gap of A Doped Linear-Chain Heisenberg Antiferromagnet

TL;DR

This paper investigates how impurity doping affects the Haldane energy gap in a spin-1 Heisenberg antiferromagnetic chain, predicting a reduction and collapse of the gap with increasing impurity concentration, verifiable by neutron scattering.

Contribution

It introduces a theoretical model using VBS and Schwinger boson mean field approximation to describe impurity effects on the Haldane gap in doped chains.

Findings

Haldane gap decreases as impurity concentration increases

Gap collapses at impurity concentration ~ 1/ξ

Model predictions can be tested via neutron scattering

Abstract

Using the valence-bond-solid (VBS) approach and the Schwinger boson mean field approximation, we study the dependence of the Haldane gap of a spin-1 linear chain Heisenberg antiferromagnet on impurity doping with different spins. The impurity spins affect the singlet pairing order parameter $\Delta $ and the constraint factor $\lambda$. As a result, the Haldane gap is reduced by a factor $ \sim n_i^{2/3}$, with $n_i$ as the impurity concentration, and eventually collapses at $n_i \sim 1/\xi$ with $\xi$ as the VBS correlation length. This theoretical prediction can be verified by neutron scattering experiments.