A thermal form factor series for the longitudinal two-point function of the Heisenberg-Ising chain in the antiferromagnetic massive regime

Abstract

We consider the longitudinal dynamical two-point function of the XXZ quantum spin chain in the antiferromagnetic massive regime. It has a series representation based on the form factors of the quantum transfer matrix of the model. The $n$th summand of the series is a multiple integral accounting for all $n$-particle $n$-hole excitations of the quantum transfer matrix. In previous works the expressions for the form factor amplitudes appearing under the integrals were either again represented as multiple integrals or in terms of Fredholm determinants. Here we obtain a representation which reduces, in the zero-temperature limit, essentially to a product of two determinants of finite matrices whose entries are known special functions. This will facilitate the further analysis of the correlation function.

61 pages, v2: typos corrected, discussion extended, references added and updated, version to appear in J. Math. Phys, v3: a few typos corrected

References in corpus (10)

• Hidden Grassmann Structure in the XXZ Model III: Introducing Matsubara direction
• The two-spinon transverse structure factor of the gapped Heisenberg antiferromagnetic chain
• Fermionic structure in the sine-Gordon model: form factors and null-vectors
• Why scalar products in the algebraic Bethe ansatz have determinant representation
• Dynamical correlation functions of the XXZ model at finite temperature
• Finite-lattice form factors in free-fermion models
• The exact two-spinon longitudinal dynamical structure factor of the anisotropic XXZ model
• Thermodynamic limit of the two-spinon form factors for the zero field XXX chain
• On convergence of form factor expansions in the infinite volume quantum Sinh-Gordon model in 1+1 dimensions
• Asymptotic analysis of the form-factors of quantum spin chains

Cited by in corpus (12)

• Correlation functions and transport coefficients in generalised hydrodynamics
• Current operators in integrable models: A review
• Preparing Bethe Ansatz Eigenstates on a Quantum Computer
• Exact real-time longitudinal correlation functions of the massive XXZ chain
• Finite temperature spin diffusion in the Hubbard model in the strong coupling limit
• Spin conductivity of the XXZ chain in the antiferromagnetic massive regime
• Thermal form-factor expansion of the dynamical two-point functions of local operators in integrable quantum chains
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots
• Finite volume form factors in integrable theories
• Dressed energy of the XXZ chain in the complex plane
• Space-like asymptotics of the thermal two-point functions of the XXZ spin-1/2 chain