# On the thermodynamic limit of form factors in the massless XXZ Heisenberg chain

Abstract : 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.
Keywords :
Document type :
Preprints, Working Papers, ...
Domain :

Cited literature [21 references]

https://hal-ens-lyon.archives-ouvertes.fr/ensl-00368568
Contributor : Jean Michel Maillet <>
Submitted on : Tuesday, March 17, 2009 - 12:06:23 AM
Last modification on : Tuesday, December 8, 2020 - 10:29:01 AM
Long-term archiving on: : Tuesday, June 8, 2010 - 11:32:06 PM

### Files

F-factor-special12.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : ensl-00368568, version 1
• ARXIV : 0903.2916

### Citation

N. Kitanine, Karol Kozlowski, Jean Michel Maillet, N. A. Slavnov, Véronique Terras. On the thermodynamic limit of form factors in the massless XXZ Heisenberg chain. 2009. ⟨ensl-00368568⟩

Record views