On the thermodynamic limit of form factor expansions of dynamical correlation functions in the massless regime of the XXZ spin $1/2$ chain

Abstract

This work constructs a well-defined and operational form factor expansion in a model having a massless spectrum of excitations. More precisely, the dynamic two-point functions in the massless regime of the XXZ spin-1/2 chain are expressed in terms of properly regularised series of multiple integrals. These series are obtained by taking, in an appropriate way, the thermodynamic limit of the finite volume form factor expansions. The series are structured in way allowing one to identify directly the contributions to the correlator stemming from the conformal-type excitations on the Fermi surface and those issuing from the massive excitations (deep holes, particles and bound states). The obtained form factor series opens up the possibility of a systematic and exact study of asymptotic regimes of dynamical correlation functions in the massless regime of the XXZ spin $1/2$ chain. Furthermore, the assumptions on the microscopic structure of the model's Hilbert space that are necessary so as to write down the series appear to be compatible with any model -- not necessarily integrable -- belonging to the Luttinger liquid universality class. Thus, the present analysis provides also the phenomenological structure of form factor expansions in massless models belonging to this universality class.

46 pages, 7 figures, V2:some explanations added. A few missprints corrected

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• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions
• Dynamical correlation functions of the XXZ model at finite temperature
• The Form Factor Program: a Review and New Results - the Nested SU(N) Off-Shell Bethe Ansatz
• Correlation functions of one-dimensional bosons at low temperature
• Microscopic approach to a class of 1D quantum critical models
• Spinon excitations in the XX chain: spectra, transition rates, observability
• Asymptotic behaviour of two-point functions in multi-species models
• Form factors of bound states in the XXZ chain

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