Thermal form factor approach to the ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime

Abstract

We use the form factors of the quantum transfer matrix in the zero-temperature limit in order to study the two-point ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime. We obtain novel form factor series representations of the correlation functions which differ from those derived either from the q-vertex-operator approach or from the algebraic Bethe Ansatz approach to the usual transfer matrix. We advocate that our novel representations are numerically more efficient and allow for a straightforward calculation of the large-distance asymptotic behaviour of the two-point functions. Keeping control over the temperature corrections to the two-point functions we see that these are of order $T^{\infty }$ in the whole antiferromagnetic massive regime. The isotropic limit of our result yields a novel form factor series representation for the two-point correlation functions of the XXX chain at zero magnetic field.

54 pages, dedicated to the memory of Petr Petrovich Kulish, v2: figures improved, v3: eqn. (50) corrected, v4: minor typos corrected

References in corpus (5)

• Dynamical structure factor at small q for the XXZ spin-1/2 chain
• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions
• On form-factor expansions for the XXZ chain in the massive regime
• Thermal form factor approach to the ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime
• Low-temperature spectrum of correlation lengths of the XXZ chain in the antiferromagnetic massive regime

Cited by in corpus (17)

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• A thermal form factor series for the longitudinal two-point function of the Heisenberg-Ising chain in the antiferromagnetic massive regime
• Thermodynamics of the spin-$1/2$ Heisenberg-Ising chain at high temperatures: a rigorous approach
• Scalar product of twisted XXX modified Bethe vectors
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• The LeClair-Mussardo series and nested Bethe Ansatz
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• Exact regimes of collapsed and extra two-string solutions in the two down-spin sector of the spin-1/2 massive XXZ spin chain
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• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish
• Space-like asymptotics of the thermal two-point functions of the XXZ spin-1/2 chain