Low-Lying Excitations in the S=1 Antiferromagnetic Heisenberg Chain

TL;DR

This study uses quantum Monte Carlo methods to analyze low-lying excitations in the S=1 antiferromagnetic Heisenberg chain, confirming the existence of finite energy gaps and repulsive interactions between excitations.

Contribution

It provides detailed numerical evidence for the energy gaps and excitation interactions in the Haldane phase, supporting the domain-wall excitation picture.

Findings

Finite energy gap between first- and second-excited states at k=π.

Second-excited state separated from ground state by a gap three times the Haldane gap.

Interactions between elementary excitations are repulsive.

Abstract

In order to confirm the picture of domain-wall excitations in the hidden antiferromagnetic order of the Haldane phase, the structure of the low-lying excitations in the S=1 antiferromagnetic Heisenberg chain is studied by a quantum Monte Carlo method. It is confirmed that there exists a finite energy gap between the first- and the second-excited states at $k=\pi$ as well as between the ground state and the first-excited state at $k=\pi$. In the thermodynamic limit, the second-excited state at $k=\pi$ is separated from the ground state by the gap which is three times as large as the Haldane gap. From the size dependences of the low-lying-excitation energies, the interactions between the elementary excitations in the excited states are concluded to be repulsive.