On the calculation of the correlation functions of the ${\mathfrak{sl}}_3$-model by means of the reduced qKZ equation

Abstract

We study the reduced density matrix of the ${\mathfrak{sl}}_3$-invariant fundamental exchange model by means of a novel reduced quantum Knizhnik-Zamolodchikov equation. This gives us insight into the algebraic structure and explicit results for correlation functions in the infinite chain ranging over up to three sites.

arXiv comment30 pages, 10 figures

References in corpus (33)

• Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field
• Correlation Functions of the XXZ model for $\Delta <-1$
• Thermodynamics of the Anisotropic Spin-1/2 Heisenberg Chain and Related Quantum Chains
• QKZ equation with |q|=1 and correlation functions of the XXZ model in the gapless regime
• Integral representations for correlation functions of the XXZ chain at finite temperature
• Integrable structure of W_3 Conformal Field Theory, Quantum Boussinesq Theory and Boundary Affine Toda Theory
• Hidden Grassmann Structure in the XXZ Model II: Creation Operators
• Hidden Grassmann structure in the XXZ model
• Quantum Spin Chains and Riemann Zeta Function with Odd Arguments
• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions
• Integral representation of the density matrix of the XXZ chain at finite temperatures
• Hidden Grassmann Structure in the XXZ Model III: Introducing Matsubara direction
• Emptiness Formation Probability and Quantum Knizhnik-Zamolodchikov Equation
• Exercises with the universal R-matrix
• Computation of static Heisenberg-chain correlators: Control over length and temperature dependence
• Reduced qKZ equation and correlation functions of the XXZ model
• Form factors in quantum integrable models with GL(3)-invariant R-matrix
• Short-distance thermal correlations in the massive XXZ chain
• Staggered Polarization of Vertex Models with $U_q(\widehat{sl}(n))$-Symmetry
• Density matrix of a finite sub-chain of the Heisenberg anti-ferromagnet
• Wronskian solutions of the T, Q and Y-systems related to infinite dimensional unitarizable modules of the general linear superalgebra gl(M|N)
• Short-distance thermal correlations in the XXZ chain
• On the physical part of the factorized correlation functions of the XXZ chain
• Yangian Double and Rational R-matrix
• Problems with using separated variables for computing expectation values for higher ranks
• Exact form factors of the SU(N) Gross-Neveu model and 1/N expansion
• Quantum groups and functional relations for higher rank
• Completeness of a fermionic basis in the homogeneous XXZ model
• Finite temperature correlation functions from discrete functional equations
• Correlation functions of the integrable $SU(n)$ spin chain
• Asymptotic behaviour of two-point functions in multi-species models
• OPE for XXX
• The critical $A_{n-1}^{(1)}$ chain

Cited by in corpus (8)

• Current operators in integrable models: A review
• Current operators in integrable spin chains: lessons from long range deformations
• Correlation functions of integrable $O(n)$ spin chains
• Vertex Models and Spin Chains in Formulas and Pictures
• Current mean values in the XYZ model
• The LeClair-Mussardo series and nested Bethe Ansatz
• On correlation functions in models related to the Temperley-Lieb algebra
• On the properties of the density matrix of the ${\mathfrak{sl}}_{n+1}$-invariant model