Equal Time Correlations in Haldane Gap Antiferromagnets

TL;DR

This paper investigates the equal time correlations and energy gaps in Haldane gap antiferromagnets using density matrix renormalization group methods, confirming theoretical models and exploring boundary effects.

Contribution

It applies DMRG to compute energy gaps and correlation functions in S=1 chains, validating nonlinear sigma model predictions and analyzing boundary excitations.

Findings

Good agreement with nonlinear sigma model predictions

Determined energy gaps and correlation lengths for different anisotropies

Analyzed boundary S=1/2 excitations in open chains

Abstract

The $S=1$ antiferromagnetic Heisenberg chain both with and without single ion anisotropy is studied. Using the recently proposed density matrix renormalization group technique we calculate the energy gaps as well as several different correlation functions. The two gaps, $\Delta_{||}, \Delta_\perp$, along with associated correlation lengths and velocities are determined. The numerical results are shown to be in good agreement with theoretical predictions derived from the nonlinear sigma model and a free boson model. We also study the $S=1/2$ excitations that occur at the ends of open chains; in particular we study the behavior associated with open boundary conditions, using a model of $S=1/2$ spins coupled to the free bosons.