Effect of a Spin-1/2 Impurity on the Spin-1 Antiferromagnetic Heisenberg Chain

TL;DR

This study investigates how a spin-1/2 impurity affects the low-energy excitations and ground state of a spin-1 antiferromagnetic Heisenberg chain, revealing impurity-induced massive modes and validating a phenomenological Hamiltonian.

Contribution

It demonstrates the impact of a spin-1/2 impurity on the Haldane gap and compares variational and numerical methods for analyzing low-lying states.

Findings

Impurity induces massive modes in the Haldane gap.

Weak impurity-host coupling makes phenomenological Hamiltonian accurate.

Variational results agree semi-quantitatively with numerical diagonalization.

Abstract

Low-lying excited states as well as the ground state of the spin-1 antiferro- magnetic Heisenberg chain with a spin-1/2 impurity are investigated by means of a variational method and a method of numerical diagonalization. It is shown that 1) the impurity spin brings about massive modes in the Haldane gap, 2) when the the impurity-host coupling is sufficiently weak, the phenomenological Hamiltonian used by Hagiwara {\it et al.} in the analysis of ESR experimental results for NENP containing a small amount of spin-1/2 Cu impurities is equivalent to a more realistic Hamiltonian, as far as the energies of the low-lying states are concerned, 3) the results obtained by the variational method are in semi-quantitatively good agreement with those obtained by the numerical diagonalization.