Correlation functions of the integrable higher-spin XXX and XXZ spin chains through the fusion method

Abstract

For the integrable higher-spin XXX and XXZ spin chains we present multiple-integral representations for the correlation function of an arbitrary product of Hermitian elementary matrices in the massless ground state. We give a formula expressing it by a single term of multiple integrals. In particular, we explicitly derive the emptiness formation probability (EFP). We assume $2s$-strings for the ground-state solution of the Bethe ansatz equations for the spin-$s$ XXZ chain, and solve the integral equations for the spin-$s$ Gaudin matrix. In terms of the XXZ coupling $\Delta$ we define $\zeta$ by $\Delta =\cos \zeta$, and put it in a region $0\le \zeta <\pi /2s$ of the gapless regime: $-1<\Delta \le 1$ ($0\le \zeta <\pi$), where $\Delta =1$ ($\zeta =0$) corresponds to the antiferromagnetic point. We calculate the zero-temperature correlation functions by the algebraic Bethe ansatz, introducing the Hermitian elementary matrices in the massless regime, and taking advantage of the fusion construction of the $R$-matrix of the higher-spin representations of the affine quantum group.

50 pages, no figure

References in corpus (23)

• Form factors of the XXZ Heisenberg spin-1/2 finite chain
• Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field
• Correlation Functions of the XXZ model for $\Delta <-1$
• QKZ equation with |q|=1 and correlation functions of the XXZ model in the gapless regime
• Functional Relations in Solvable Lattice Models I: Functional Relations and Representation Theory
• On the quantum inverse scattering problem
• Integral representations for correlation functions of the XXZ chain at finite temperature
• Spinons in Magnetic Chains of Arbitrary Spins at Finite Temperatures
• Functional Relations in Solvable Lattice Models II
• Correlation functions of the higher spin XXX chains
• Level two irreducible representations of $U_q({\widehat{sl}}_2)$, vertex operators, and their correlations
• Form factors of integrable Heisenberg (higher) spin chains
• The L(sl_2) symmetry of the Bazhanov-Stroganov model associated with the superintegrable chiral Potts model
• The Vertex-Face Correspondence and Correlation Functions of the Fusion Eight-Vertex Model I: The General Formalism
• N-point Correlation Functions of the Spin-1 XXZ Model
• On the algebraic Bethe Ansatz approach to the correlation functions of the XXZ spin-1/2 Heisenberg chain
• Free Field Representation of Quantum Affine Algebra $U_q\widehat{s{l}_2}$ and Form Factors in Higher Spin XXZ Model
• Finite temperature density matrix and two-point correlations in the antiferromagnetic XXZ chain
• Form factors of integrable higher-spin XXZ chains and the affine quantum-group symmetry
• Algebraic Bethe Ansatz for U(1) Invariant Integrable Models: The Method and General Results
• Algebraic Bethe ansatz for U(1) Invariant Integrable Models: Compact and non-Compact Applications
• Correlation functions of the spin-1 analog of the XXZ model
• Determinant Formula for the Solutions of the Quantum Knizhnik-Zamolodchikov Equation with |q|=1

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