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Physics Letters A

Systematic approach for spin correlations in Heisenberg systems for all temperatures

Armin Bunde A, Sigurd Diederich, W. Biem

Published Nov 1, 1975• 6 citations
Publisher
DOI
10.1016/0375-9601(75)90154-1

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By adopting the concept of the geometric measure of quantum discord, we explore the property of quantum correlation in the two-spin Heisenberg model, gain the analytic expression of quantum discord in the general case, and discuss the influences of the coupling constant, temperature, the intensity of the external magnetic field on magnitude of the quantum correlation. The corresponding scheme of tuning quantum correlation is also given in this paper. In addition, we find that quantum discord has a sudden transition in the lower temperature. Results show that adjusting systematic parameters, which are temperature, coupling strength, magnetic field intensity, etc, is an effective way to control the value of quantum correlation in the double spin Heisenberg model system. This provides a certain reference and significant guidance for the precise control of quantum discord and realizing the teleportation of quantum state and the design of quantum logic gates.
The maximum Lyapunov exponent (MLE) is evaluated as a function of temperature in the isotropic Heisenberg chain. At low temperatures the MLE varies almost quadratically with temperature; it corresponds closely with ${\mathrm{\ensuremath{\tau}}}_{1\mathrm{/}2}^{\mathrm{\ensuremath{-}}1}$, the rate at which the local self-correlation decays to half its initial value. At higher temperatures, the MLE saturates at a value close to 1/2 in the limit of large chain lengths. The strong stochasticity threshold (defined by the change of slope of the MLE) parallels closely the transition from predominantly ballistic to predominantly diffusive behavior of the self-correlation and the concomitant steep increase in ${\mathrm{\ensuremath{\tau}}}_{1\mathrm{/}2}^{\mathrm{\ensuremath{-}}1}$. The complete Lyapunov spectrum has been derived for a chain of 18 spins; deviations from linearity occurring at infinite temperature suggest that the chaoticity of the system is incomplete. Finally, it is suggested that a systematic study of finite-size effects might be useful in deciding the issue of anomalous versus conventional spin diffusion.