N-point Correlation Functions of the Spin-1 XXZ Model

Abstract

We extend the recent approach of M. Jimbo, K. Miki, T. Miwa, and A. Nakayashiki to derive an integral formula for the N-point correlation functions of arbitrary local operators of the antiferromagnetic spin-1 XXZ model. For this, we realize the quantum affine symmetry algebra $U_q(su(2{)}_2)$ of level 2 and its corresponding type I vertex operators in terms of a deformed bosonic field free of a background charge, and a deformed fermionic field. Up to GSO type projections, the Fock space is already irreducible and therefore no BRST projections are involved. This means that no screening charges with their Jackson integrals are required. Consequently, our N-point correlation functions are given in terms of usual classical integrals only, just as those derived by Jimbo et al in the case of the spin-1/2 XXZ model through the Frenkel-Jing bosonization of $U_q(su(2{)}_1)$.

23 pages (Minor mistake in N-point fn. formula corrected)

References in corpus (4)

• Correlation Functions of the XXZ model for $\Delta <-1$
• Diagonalization of the XXZ Hamiltonian by Vertex Operators
• Quantum affine symmetry in vertex models
• Uniqueness of the bosonization of the $U_q(su(2{)}_k)$ quantum current algebra

Cited by in corpus (22)

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• Form factors of integrable Heisenberg (higher) spin chains
• The Vertex-Face Correspondence and Correlation Functions of the Fusion Eight-Vertex Model I: The General Formalism
• Correlation functions of the integrable higher-spin XXX and XXZ spin chains through the fusion method
• The twisted quantum affine algebra $U_q(A^{(2)_2)$ and correlation functions of the Izergin-Korepin model
• Highest weight representations of $U_q(\widehat{sl}(2|1))$ and correlation functions of the q-deformed supersymmetric t-J model
• Correlation functions of the integrable $SU(n)$ spin chain
• Correlation functions of the integrable isotropic spin-1 chain at finite temperature
• Correlation functions of the integrable isotropic spin-1 chain: algebraic expressions for arbitrary temperature
• Correlation functions of integrable $O(n)$ spin chains
• Computation of dynamical correlation functions of the spin-1 Babujan-Takhtajan chain
• Correlation functions of the integrable spin-s chain
• Symmetry protected topological phases beyond groups: The q-deformed bilinear-biquadratic spin chain
• Level-one Highest Weight Representation of $U_q[\widehat{sl(N|1)}]$ and Bosonization of the Multi-component Super t-J Model
• Spinon excitations in the spin-1 XXZ chain and hidden supersymmetry
• Finite size effects and 2-string deviations in the spin-1 XXZ chains
• A Quantum Analogue of the $\mathcal{Z}$ Algebra
• q-deformed Supersymmetric t-J Model with a Boundary
• Sum rules for four-spinon dynamic structure factor in XXX model
• General Formalism For the BRST Symmetry
• Form factors of spin 1 analogue of the eight-vertex model
• Quantum Group U_q(sl(2)) Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain