Journal of Physics C Solid State Physics

A note on higher moments and spectral shape for a classical Heisenberg chain

Hiroyuki Mashiyama

Published Aug 14, 1979• 4 citations

Abstract

The relaxation function and the spectral shape are investigated theoretically for a classical Heisenberg magnetic chain. In order to reproduce the spectrum, moments of the spin correlation function are calculated rigorously up to the eighth order for the magnetic chain. Proper continuations are introduced in the continued fraction expansion of spin-pair correlation function.

DOI: 10.1088/0022-3719/12/15/015

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Journal of Physics C Solid State Physics

A note on higher moments and spectral shape for a classical Heisenberg chain

Hiroyuki Mashiyama

Published Aug 14, 1979• 4 citations

Publisher

Abstract

DOI: 10.1088/0022-3719/12/15/015

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T=0

result, simple approximations are used to calculate the spectrum. We show rigorously that the time-dependent correlation function is different for ferro-and antiferromagnetic coupling if $T\ensuremath{\ne}0$.

\frac{T}{J{S}^{2}}

and

\frac{1}{S}

. The results include an expression for the spin correlation function in the antiferromagnetic ground state and a discussion of changes in line shape, due to quantum effects, for short-wavelength magnons as observed in neutron scattering experiments.

{S}_{T}^{z}

) up to saturation for each chain. From a knowledge of the eigenvector corresponding to the lowest eigenstate for each

{S}_{T}^{z}

, 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.