Document Type

Article

Date of Original Version

10-1-1985

Abstract

Extensive numerical studies have been performed on Heisenberg antiferromagnetic chains of spin (1/2) (up to N=20), spin 1 (N=14), spin (3/2) (N=10), and spin 2 (N=8). With use of the Lanczös technique, primarily, the two lowest-lying eigenvalues have been calculated for all values of wave vector q and all values of magnetization (SzT) up to saturation for each chain. From a knowledge of the eigenvector corresponding to the lowest eigenstate for each SzT, the T=0 spin-pair correlation functions have also been calculated as a function of field. We find a most unusual quantum-classical crossover phenomenon. It shows up in greatest detail in the field-dependent dispersion spectra, but the consequences are consistently manifested in the behavior of the T=0 magnetization isotherms and in the correlations both in real space and the Fourier transforms in q space. The additional data relevant to behavior in a field have allowed us to extend previous numerical studies of Heisenberg antiferromagnetic chains with higher spin whose purpose was to examine the validity of the Haldane conjecture. The Haldane conjecture implies that Heisenberg antiferromagnetic chains with integer spin have a gap in their excitation spectrum whereas chains with half-integer spin do not. While no feature of our extended investigations is in conflict with the conjecture, unusual features associated apparently with very slow convergence make the outcome less than conclusive. It appears that calculations on significantly longer chains are required to observe with confidence the large-N asymptotic limiting behavior.

Publisher Statement

© 1985 American Physical Society. All rights reserved.

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