Finite temperature correlation functions from discrete functional equations

Abstract

We present a new approach to the static finite temperature correlation functions of the Heisenberg chain based on functional equations. An inhomogeneous generalization of the n-site density operator is considered. The lattice path integral formulation with a finite but arbitrary Trotter number allows to derive a set of discrete functional equations with respect to the spectral parameters. We show that these equations yield a unique characterization of the density operator. Our functional equations are a discrete version of the reduced q-Knizhnik-Zamolodchikov equations which played a central role in the study of the zero temperature case. As a natural result, and independent of the arguments given by Jimbo, Miwa, and Smirnov (2009) we prove that the inhomogeneous finite temperature correlation functions have the same remarkable structure as for zero temperature: they are a sum of products of nearest-neighbor correlators.

24 pages, 11 figures

References in corpus (38)

• 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 $\Delta <-1$
• 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
• Unified Approach to Thermodynamic Bethe Ansatz and Finite Size Corrections for Lattice Models and Field Theories
• Integral representations for correlation functions of the XXZ chain at finite temperature
• Two-spinon dynamic structure factor of the one-dimensional S=1/2 Heisenberg antiferromagnet
• Hidden Grassmann Structure in the XXZ Model II: Creation Operators
• Master equation for spin-spin correlation functions of the XXZ chain
• 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
• Form factor approach to the asymptotic behavior of correlation functions in critical models
• Integrability of quantum chains: theory and applications to the spin-1/2 $XXZ$ chain
• Hidden Grassmann Structure in the XXZ Model III: Introducing Matsubara direction
• Emptiness Formation Probability and Quantum Knizhnik-Zamolodchikov Equation
• Exact two-spin dynamic structure factor of the one-dimensional s=1/2 Heisenberg-Ising antiferromagnet
• Density matrices for finite segments of Heisenberg chains of arbitrary length
• Thermodynamic limit of particle-hole form factors in the massless XXZ Heisenberg chain
• Algebraic representation of correlation functions in integrable spin chains
• Computation of static Heisenberg-chain correlators: Control over length and temperature dependence
• The Spin-Exchange Dynamical Structure Factor of the S=1/2 Heisenberg Chain
• Hidden Grassmann Structure in the XXZ Model IV: CFT limit
• Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field
• Reduced qKZ equation and correlation functions of the XXZ model
• Factorization of multiple integrals representing the density matrix of a finite segment of the Heisenberg spin chain
• The two-spinon transverse structure factor of the gapped Heisenberg antiferromagnetic chain
• Density matrix of a finite sub-chain of the Heisenberg anti-ferromagnet
• Correlation functions of the higher spin XXX chains
• Correlation functions of the spin-1/2 anti-ferromagnetic Heisenberg chain: exact calculation via the generating function
• Evaluation of Dynamic spin structure factor for the spin-1/2 XXZ chain in a magnetic field
• On the physical part of the factorized correlation functions of the XXZ chain
• First principle approach to correlation functions of spin-1/2 Heisenberg chain : fourth-neighbor correlators
• On the spin-spin correlation functions of the XXZ spin-1/2 infinite chain
• Spinon excitations in the XX chain: spectra, transition rates, observability
• Correlation functions of the integrable isotropic spin-1 chain at finite temperature

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