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Physical review. B, Condensed matter

Continued-fraction formalism applied to the spin-1/2XYZmodel

Edson Sardella

Published Jun 1, 1991• 4 citations
Publisher

Abstract

In this paper, we evaluate the correlation functions of the spin-1/2 XYZ model for some particular cases by using the Mori continued-fraction formalism. The results are exactly the same as those well-known ones. This removes any doubt about the convergence of the continued fraction recently raised by some authors.
DOI
10.1103/physrevb.43.13653

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Three decades ago, the quantum Langevin-like equation (Mori formula) was used to reformulate the linear response theory (Kubo formula) in the continued fraction formalism. Since then, the Mori formula has often been used to evaluate transport coefficients, but only within the Born approximation. Very recently, a rigorous closed-form solution to the Mori formula for transport coefficients has been obtained. In the present study, we prove the equivalence of the closed-form solution to the Mori formula and the Kubo formula using the general relations between correlation functions and then comment on the Born approximation.
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Dynamical correlations in simple quantum spin models can be conveniently studied via the continued fraction formalism in which the Laplace transformed dynamical two-point correlation can be written as C(z) = 1/(z + Δ1/(z + Δ2/(z + ..to ∞))), where Δn’s are functions of static correlations. Very often, for systems without any natural dominant characteristic frequencies, as n increases, Δn ≊ κnα, α=0 or 1, κ being some constant, for large n for simple quantum spin systems. It is suggested that this property of Δn’s could be related to some underlying ‘‘nearly noninteracting fermionic nature’’ of these quantum spin systems.