Impurity Energy Level Within The Haldane Gap

TL;DR

This study uses numerical methods to identify impurity-induced bound states within the Haldane gap of a 1D antiferromagnetic spin-1 chain, revealing how impurity strength affects the energy levels.

Contribution

The paper demonstrates the existence and behavior of impurity energy levels in the Haldane gap, including the threshold effect for impurity bond strength, using density matrix renormalization group calculations.

Findings

Impurity energy levels appear near the Haldane gap in the spin chain.

No threshold for impurity levels when J' < J, levels shift gradually.

A threshold exists for J' > J, around 0.3, beyond which impurity levels emerge.

Abstract

An impurity bond $J{'}$ in a periodic 1D antiferromagnetic, spin 1 chain with exchange $J$ is considered. Using the numerical density matrix renormalization group method, we find an impurity energy level in the Haldane gap, corresponding to a bound state near the impurity bond. When $J{'}<J$ the level changes gradually from the edge of the Haldane gap to the ground state energy as the deviation $dev=(J-J{'})/J$ changes from 0 to 1. It seems that there is no threshold. Yet, there is a threshold when $J{'}>J$. The impurity level appears only when the deviation $dev=(J{'}-J)/J{'}$ is greater than $B_{c}$, which is near 0.3 in our calculation.