Impurity state in Haldane gap for S=1 Heisenberg antiferromagnetic chain with bond doping

TL;DR

This paper uses a novel impurity density matrix renormalization group method to analyze how bond doping affects low energy states in a S=1 Heisenberg antiferromagnetic chain, revealing a new impurity state in the Haldane gap.

Contribution

It introduces a new computational scheme to quantitatively study impurity effects in the Haldane gap of S=1 chains, explaining experimental observations.

Findings

A new impurity state appears in the Haldane gap when J'/J<1.

The impurity state emerges only if J'/J exceeds a critical value.

The system behavior is non-perturbative for 1 ≤ J'/J ≤ γ_c.

Abstract

Using a new impurity density matrix renormalization group scheme, we establish a reliable picture of how the low lying energy levels of a $S=1$ Heisenberg antiferromagnetic chain change {\it quantitatively} upon bond doping. A new impurity state gradually occurs in the Haldane gap as $J' < J$, while it appears only if $J'/J>\gamma_c$ with $1/\gamma_c=0.708$ as $J'>J$. The system is non-perturbative as $1\leq J'/J\leq\gamma_c$. This explains the appearance of a new state in the Haldane gap in a recent experiment on Y$_{2-x}$Ca$_x$BaNiO$_5$ [J.F. DiTusa, et al., Phys. Rev. Lett. 73 1857(1994)].