Haldane Gap and Hidden Order in the S=2 Antiferromagnetic Quantum Spin Chain

TL;DR

This study confirms Haldane's conjecture for the S=2 antiferromagnetic chain, revealing a finite spin gap, hidden topological order, and effective edge spins, using advanced numerical methods.

Contribution

The paper provides the first detailed numerical evidence of a finite gap and hidden order in the S=2 chain, supporting the valence-bond solid model.

Findings

Finite spin gap of approximately 0.085J

Finite correlation length of about 49 lattice spacings

Presence of effective free spin-1 states at chain ends

Abstract

We have investigated Haldane's conjecture for the S=2 isotropic antiferromagnetic quantum spin chain with nearest-neighbor exchange J. Using a density matrix renormalization group algorithm for chains up to L=350 spins, we find in the thermodynamic limit a finite spin gap of Delta = 0.085(5)J and a finite spin-spin correlation length xi = 49(1) lattice spacings. We establish the ground state energy per bond to be E_0=-4.761248(1)J. We show that the ground state has a hidden topological order that is revealed in a nonlocal string correlation function. This means that the physics of the S=2 chain can be captured by a valence-bond solid description. We also observe effective free spin-1 states at the ends of an open S=2 chain.