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arXiv:cond-mat/0104120 · Physical review. B, Condensed matter

Lineshapes of dynamical correlation functions in Heisenberg chains

Ralph Werner, Andreas Klümper

Published Oct 10, 2001• 2 citations
arXivHTMLPDF

Abstract

We calculate lineshapes of correlation functions by use of complete diagonalization data of finite chains and analytical implications from conformal-field theory, density of states, and Bethe ansatz. The numerical data have different finite-size accuracy in the cases of the imaginary and real parts in the frequency and time representations of spin-correlation functions, respectively. The low-temperature, conformally invariant regime crosses over at ${T}^{*}\ensuremath{\approx}0.7J$ to a diffusive regime that in turn connects continuously to the high-temperature, interacting-fermion regime. The first-moment sum rule is determined.

DOI
10.1103/physrevb.64.174414

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We compute all dynamical spin–spin correlation functions for the spin-1/2 XXZ anisotropic Heisenberg model in the gapless antiferromagnetic regime at zero temperature, using numerical sums of exact determinant representations for form factors of spin operators on the lattice. Contributions from intermediate states containing many particles and string (bound) states are included. We present modified determinant representations for the form factors valid in the general case with string solutions to the Bethe equations. Our results are such that the available sum rules are saturated to high precision. We Fourier transform our results back to real space, allowing us in particular to make a comparison with known exact formulae for equal-time correlation functions for small separations in zero field, and with predictions for the zero-field asymptotics from conformal field theory.
We investigate transport in several translationally invariant spin-12\frac{1}{2}21​ chains in the limit of high temperatures. We concretely consider spin transport in the anisotropic Heisenberg chain, the pure Heisenberg chain within an alternating field, and energy transport in an Ising chain which is exposed to a tilted field. Our approach is essentially based on a connection between the evolution of the variance of an inhomogeneous nonequilibrium density and the current-autocorrelation function at finite times. Although this relationship is not restricted to the case of diffusive transport, it allows to extract a quantitative value for the diffusion constant in that case. By means of numerically exact diagonalization we indeed observe diffusive behavior in the considered spin chains for a range of model parameters and confirm the diffusion coefficients which were obtained for these systems from nonequilibrium bath scenarios.
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