Exact Form-Factor Results for the Longitudinal Structure Factor of the Massless XXZ Model in Zero Field

Caux Jean-Sébastien

Konno Hitoshi

Sorrell Mark

Weston Robert

Journal of Statistical Mechanics: Theory and Experiment

We consider the XXZ quantum spin chain in its massless, disordered regime at zero field. We derive an exact expression for the two-spinon form-factor of Sz = 1/2σz by taking a limit of the massive XYZ form-factors found by Lashkevich and by Lukyanov and Terras. This result is used to find the two-spinon contribution to the spectral decomposition of the longitudinal structure factor Szz(k, w). We find that this contribution provides an accurate approximation to the full structure factor over a wide range of the anisotropy parameter. The asymptotic behaviour of Szz(k, w) is computed as the upper and lower w thresholds of the two-spinon (w, k) band are approached, and an analysis of the region of validity of this threshold behaviour is performed. Our results reproduce and refine existing threshold behaviour predictions and extend these results to an accurate description throughout the two-spinon continuum.

Physics [ 420 ]

eng

IOP Publishing Ltd

This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。

[ISSN] 1742-5468

[DOI] 10.1088/1742-5468/2012/01/P01007

[DOI] https://doi.org/10.1088/1742-5468/2012/01/P01007