Impurities in $s=1$ Heisenberg Antiferromagnets

TL;DR

This study investigates how local impurities affect the energy spectrum of the $s=1$ Heisenberg Antiferromagnet, revealing bound states in the Haldane gap depending on impurity type and coupling strength, with implications for experimental observations.

Contribution

It provides a detailed analysis of impurity-induced bound states in the $s=1$ Heisenberg chain using DMRG, highlighting the conditions under which these states appear, which was not fully understood before.

Findings

Bound states localized at impurities for strong or weak couplings.

No in-gap states near the uniform coupling $J'=J$.

Qualitative agreement with experiments on doped nickel compounds.

Abstract

The $s=1$ Heisenberg Antiferromagnet is studied in the presence of two kinds of local impurities. First, a perturbed antiferromagnetic bond with $J'\ne J$ at the center of an even-length open chain is considered. Using the density matrix renormalization group method we find that, for sufficiently strong or weak $J'$, a bound state is localized at the impurity site, giving rise to an energy level in the Haldane gap. The energy of the bound state is in agreement with perturbative results, based on $s=1/2$ chain-end excitations, both in the weak and strong coupling limit. In a region around the uniform limit, $J'=J$, no states are found with energy below the Haldane gap. Secondly, a $s=1/2$ impurity at the center of an otherwise even-length open chain is considered. The coupling to the $s=1/2$ impurity is varied. Bound states in the Haldane gap are found {\it only} for sufficiently weak (antiferromagnetic) coupling. For a $s=1/2$ impurity coupled with a strong (antiferromagnetic) bond, {\it no} states are found in the Haldane. Our results are in good qualitative agreement with recent experiments on doped NENP and Y$_2$BaNiO$_5$.