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Exact Diag. Study of the 1D Disordered XXZ Model

K. J. Runge·G. T. Zimanyi
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Abstract

We investigate the one-dimensional quantum $XXZ$ model in the presence of diagonal disorder. Recently the model has been analyzed with the help of field-theoretical renormalization group methods, and a phase diagram has been predicted. We study the model with exact diagonalization techniques up to chain lengths of 16 sites. Using finite-size scaling methods we estimate critical exponents and the phase diagram and find reasonably good agreement with the field-theoretical results, namely, that any amount of disorder destroys the superfluidity for $XXZ$ anisotropy $Δ$ between $ -1/2 $ and $1$, while the superfluidity persists to finite disorder strength for $ -1 < Δ< -1/2$ and then undergoes a Kosterlitz-Thouless type transition.

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K. J. Runge, G. T. Zimanyi. 1993-12-01. Exact Diag. Study of the 1D Disordered XXZ Model. https://arxiv.org/abs/cond-mat/9312002

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