Spectral expansion for finite temperature two-point functions and clustering

Abstract

Recently, the spectral expansion of finite temperature two-point functions in integrable quantum field theories was constructed using a finite volume regularization technique and the application of multidimensional residues. In the present work, the original calculation is revisited. By clarifying some details in the residue evaluations, we find and correct some inaccuracies of the previous result. The final result for contributions involving no more than two particles in the intermediate states is presented. The result is verified by proving a symmetry property which follows from the general structure of the spectral expansion, and also by numerical comparison to the discrete finite volume spectral sum. A further consistency check is performed by showing that the expansion satisfies the cluster property up to the order of the evaluation.

38 pages, 1 eps figures

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Cited by in corpus (13)

• Exact large-scale correlations in integrable systems out of equilibrium
• How order melts after quantum quenches
• Overlap singularity and time evolution in integrable quantum field theory
• Finite temperature spin dynamics in a perturbed quantum critical Ising chain with an $E_8$ symmetry
• LeClair-Mussardo series for two-point functions in Integrable QFT
• Finite temperature dynamics in gapped 1D models in the sine-Gordon family
• Exact finite volume expectation values of local operators in excited states
• Finite temperature one-point functions in non-diagonal integrable field theories: the sine-Gordon model
• An integrable spin chain with Hilbert space fragmentation and solvable real time dynamics
• Local dynamics and thermal activation in the transverse-field Ising chain
• Long-time divergences in the nonlinear response of gapped one-dimensional many-particle systems
• Mixed-state form factors of $U(1)$ twist fields in the Dirac theory
• A diagrammatic approach towards the thermodynamics of integrable systems