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On the thermodynamic limit of form factors in the massless XXZ Heisenberg chain
N. Kitanine1, Karol K. Kozlowski2, Jean Michel Maillet2, N. A. Slavnov3, Véronique Terras2, 4
(17/03/2009)

We consider the problem of computing form factors of the massless XXZ Heisenberg spin-1/2 chain in a magnetic field in the (thermodynamic) limit where the size M of the chain becomes large. For that purpose, we take the particular example of the matrix element of the third component of spin between the ground state and an excited state with one particle and one hole located at the opposite ends of the Fermi interval (umklapp-type term). We exhibit its power-law decrease in terms of the size of the chain M , and compute the corresponding exponent and amplitude. As a consequence, we show that this form factor is directly related to the amplitude of the leading oscillating term in the long-distance asymptotic expansion of the two-point correlation function of the third component of spin.
1 :  LPTM - Laboratoire de Physique Théorique et Modélisation
2 :  Phys-ENS - Laboratoire de Physique de l'ENS Lyon
3 :  SMI - Steklov Mathematical Institute
4 :  LPTA - Laboratoire de Physique Théorique et Astroparticules
Physique/Physique des Hautes Energies - Théorie

Physique/Physique mathématique

Mathématiques/Physique mathématique

Physique/Matière Condensée/Mécanique statistique
Quantum integrable models – spin chain – form factors – correlation functions – asymptotic analysis
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