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

Abstract

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 $S^z=1/2{\sigma }^z$ 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 $S^{zz}(k,w)$. 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 $S^{zz}(k,w)$ 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.

39 pages, 10 figures, dedicated to Prof. M. Jimbo

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• Dimer correlation amplitudes and dimer excitation gap in spin-1/2 XXZ and Heisenberg chains
• A thermal form factor series for the longitudinal two-point function of the Heisenberg-Ising chain in the antiferromagnetic massive regime
• Low-energy spin dynamics in rare-earth perovskite oxides
• On singularities of dynamic response functions in the massless regime of the XXZ spin-1/2 chain
• Spin conductivity of the XXZ chain in the antiferromagnetic massive regime
• The dynamic structure factor in impurity-doped spin chains
• Momentum-resolved time evolution with matrix product states
• Thermodynamic limit of the two-spinon form factors for the zero field XXX chain
• Asymptotic analysis of the form-factors of quantum spin chains
• Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots
• Self-Consistent Random Phase Approximation from Projective Truncation Approximation Formalism