arXiv:hep-th/9307090 · International Journal of Modern Physics A

ANNIHILATION POLES FOR FORM FACTORS IN THE XXZ MODEL

S. PAKULIAK

Published May 10, 1994• 7 citations

Abstract

The annihilation poles for the form factors in the XXZ model are studied using vertex operators introduced in Ref. 1. An annihilation pole is the property of form factors according to which the residue of the 2n-particle form factor in such a pole can be expressed through linear combination of the (2n−2)-particle form factors. To prove this property we use the bosonization of the vertex operators in the XXZ model which was invented in Ref. 2.

DOI: 10.1142/s0217751x94000881

Related papers

Traces of creating-annihilating operators and Fredholm's formulas

Alexander V Chervov

We prove the formula for the traces of certain class of operators in bosonic and fermionic Fock spaces. Vertex operators belong to this class. Traces of vertex operators can be used for calculation of correlation functions and formfactors of integrable models (XXZ, Sine-Gordon, etc.), that is why we are interested in this problem. Also we show that Fredholm's minor and determinant can be expressed by such traces. We obtain a short proof of the Fredholm's formula for the solution of an integral equation.

Mar 9, 19974 citations

A Vertex Operator Approach for Form Factors of Belavin's (Z/nZ)-Symmetric Model and Its Application

Yas-Hiro Quano

A vertex operator approach for form factors of Belavin's (Z/nZ)-symmetric model is constructed on the basis of bosonization of vertex operators in the A (1) n-1 model and vertex-face transformation.As simple application for n = 2, we obtain expressions for 2m-point form factors related to the σ z and σ x operators in the eight-vertex model.

arXiv:1010.4382Symmetry Integrability and Geometry Methods and ApplicationsJan 15, 20110 citations

Traces of creation-annihilation operators and Fredholm's formulas

Alexander V Chervov

arXiv:q-alg/9703017Mar 9, 19970 citations

Annihilation poles of a Smirnov-type integral formula for solutions to the quantum Knizhnik-Zamolodchikov equation

T Kojima, Kunio Miki, Yas-Hiro Quano

We consider the recently obtained integral representation of the quantum Knizhnik-Zamolodchikov equation of level 0. We obtain the condition for the integral kernel such that these solutions satisfy three axioms for the form factor in the manner of Smirnov. We discuss the relation between this integral representation and the form factor of the XXZ spin chain.

arXiv:hep-th/9501138Journal of Physics A Mathematical and GeneralJun 21, 19954 citations

EIGENSTATES OF LINEAR COMBINATIONS OF TWO-BOSON CREATION AND ANNIHILATION OPERATORS: AN ALGEBRAIC APPROACH

P. SHANTA, S. Chaturvedi, V. SRINIVASAN

Eigenstates of the linear combinations a2+βa†2 and ab+βa†b†of two-boson creation and annihilation operators are presented. The algebraic procedure given here is based on the work of Shanta et al. [Phys. Rev. Lett.72, 1447, (1994)] for constructing eigenstates of generalized annihilation operators. Expressions for the overlaps of these states with the number states, the coherent states and the squeezed states are given in a closed form.

arXiv:quant-ph/9608034Modern Physics Letters ASep 21, 19966 citations

Form factors and vertex operators in the XYZ antiferromagnet

Yas-Hiro Quano

This article summarizes my talk on form factors in the reflectionless eight-vertex model, given in the conference 'Elliptic Integrable Systems', held as a part of RIMS Project, Department of Mathematics, Kyoto University, November 8-11, 2004.It is shown that the form factors of σ z in the eight-vertex model at the so-called reflectionless points can be expressed in terms of the sum of theta functions without any integrals.

Jan 1, 20050 citations