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arXiv:cond-mat/9307028 · Europhysics Letters (EPL)

Matrix Product Ground States for One-Dimensional Spin-1 Quantum Antiferromagnets

Andreas Klümper, Andreas Schadschneider, J. Zittartz

Published Nov 1, 1993• 274 citations
arXivHTMLPDF

Abstract

We have found the exact ground state for a large class of antiferromagnetic spin-1 models with nearest-neighbour interactions on a linear chain. All ground-state properties can be calculated. The ground state is determined as a matrix product of individual site states and has the properties of the Haldane scenario.
DOI
10.1209/0295-5075/24/4/010

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We present a method of constructing matrix-product (MP) states and apply it to the ground state of the Heisenberg spin chain with alternating spins 1 and and antiferromagnetic exchange interactions between nearest neighbors (the simplest example of a quantum ferrimagnet). The elementary matrix state is constructed in a way that ensures given transformational properties under rotations, which allows one to fix the total spin, and its z projection, of the entire MP wave function. We compare the variational MP results with the numerical results obtained through a quantum Monte Carlo method; the agreement is found to be within 0.4% for the ground-state energy and 5% for the correlation functions.