Deformation of the Wakimoto Construction

Abada, A.; Bougourzi, A. H.; Gradechi, M.A. El

doi:10.1142/s0217732393000738

Cited by 35 publications

(89 citation statements)

References 18 publications

(32 reference statements)

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“…[9,10,11,12]. This vertex plays a role of an annihilation operator (it's anti-pode dual plays a creation operator) of physical particle in the spin k/2 XXZ model.…”

mentioning

confidence: 99%

Free-field representation of the quantum affine algebra and form factors in the higher-spin XXZ model

Konno¹

1994

Nuclear Physics B

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We consider the spin k/2 XXZ model in the antiferomagnetic regime using the free field realization of the quantum affine algebra U q ( sl 2 ) of level k. We give a free field realization of the type II q-vertex operator, which describes creation and annihilation of physical particles in the model. By taking a trace of the type I and the type II q-vertex operators over the irreducible highest weight representation of U q ( sl 2 ), we also derive an integral formula for form factors in this model. Investigating the structure of poles, we obtain a residue formula for form factors, which is a lattice analog of the higher spin extension of the Smirnov's formula in the massive integrable quantum field theory. This result as well as the quantum deformation of the Knizhnik-Zamolodchikov equation for form factors shows a deep connection in the mathematical structure of the integrable lattice models and the massive integrable quantum field theory.

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“…[9,10,11,12]. This vertex plays a role of an annihilation operator (it's anti-pode dual plays a creation operator) of physical particle in the spin k/2 XXZ model.…”

mentioning

confidence: 99%

Free-field representation of the quantum affine algebra and form factors in the higher-spin XXZ model

Konno¹

1994

Nuclear Physics B

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“…where W r is a certain submodule of F r specified as a kernel of a certain operator, called qWakimoto module [15,12,13,11,1], V (l) is the irreducible representation of U q (sl 2 ) with spin l/2 and V…”

Section: Remarkmentioning

confidence: 99%

Free Field Approach to Solutions of the Quantum Knizhnik-Zamolodchikov Equations

Kuroki¹

2008

SIGMA

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“…One had to wait for advances in two-dimensional conformal field theory to see how the infinite two-dimensional conformal symmetry allows the computation of correlation functions of the so-called vertex operators, using bosonization techniques [33]. The same strategy was then applied to quantum spin chains once it became clear how to adapt the bosonization method to deformed commutation relations between creation and annihilation operators [34,35,36,37]. For the Heisenberg model, actual formal manipulations are made in the context of the equivalent six-vertex model where vertex operators are defined in the framework of the infinite-dimensional representation of the quantum group.…”

Section: Introductionmentioning

confidence: 99%

Sum rules for four-spinon dynamic structure factor in XXX model

Lakhal¹,

Abada²

2005

Physica B: Condensed Matter

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In the context of the antiferromagnetic spin 1/2 Heisenberg quantum spin chain (XXX model), we estimate the contribution of the exact four-spinon dynamic structure factor S 4 by calculating a number of sum rules the total dynamic structure factor S is known to satisfy exactly. These sum rules are: the static susceptibility, the integrated intensity, the total integrated intensity, the first frequency moment and the nearest-neighbor correlation function. We find that the contribution of S 4 is between 1% and 2.5%, depending on the sum rule, whereas the contribution of the exact two-spinon dynamic structure factor S 2 is between 70% and 75%. This is consistent with the expected scattering weight of states from outside the spin-wave continuum. The calculations are numerical and Monte Carlo based. Good statistics are obtained.

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Deformation of the Wakimoto Construction

Cited by 35 publications

References 18 publications

Free-field representation of the quantum affine algebra and form factors in the higher-spin XXZ model

Free-field representation of the quantum affine algebra and form factors in the higher-spin XXZ model

Free Field Approach to Solutions of the Quantum Knizhnik-Zamolodchikov Equations

Sum rules for four-spinon dynamic structure factor in XXX model

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