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CRC Press eBooks

Regular fractal structure of the energy matrix in ID Heisenberg open spin- 1 2 chains

Feng Pan, J. P. Draayer, L -R Dai, D Zhang

Published Nov 30, 2003• 0 citations
Publisher

Abstract

A permutation group approach to a one-dimensional Heisenberg open spin-j chain with nearest neighbor interactions is studied. Regular fractal structures appear in matrices of the Hamiltonian constructed under the outer-product basis of the permutation group, which enables one to solve the eigenvalue problem in a systematic manner.
DOI
10.1201/9781482269079-73

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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.