LeClair-Mussardo series for two-point functions in Integrable QFT

Abstract

We develop a well-defined spectral representation for two-point functions in relativistic Integrable QFT in finite density situations, valid for space-like separations. The resulting integral series is based on the infinite volume, zero density form factors of the theory, and certain statistical functions related to the distribution of Bethe roots in the finite density background. Our final formulas are checked by comparing them to previous partial results obtained in a low-temperature expansion. It is also show that in the limit of large separations the new integral series factorizes into the product of two LeClair-Mussardo series for one-point functions, thereby satisfying the clustering requirement for the two-point function.

arXiv comment27 pages, v2: minor modifications, a note and a reference added

References in corpus (25)

• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• Generalized Gibbs ensemble in integrable lattice models
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Form factors of the XXZ Heisenberg spin-1/2 finite chain
• Finite Temperature Correlation Functions in Integrable QFT
• Form factors in finite volume II:disconnected terms and finite temperature correlators
• Asymptotic factorisation of form factors in two-dimensional quantum field theory
• Form factors in finite volume I: form factor bootstrap and truncated conformal space
• Solution of the quantum inverse problem
• Finite-temperature lineshapes in gapped quantum spin chains
• A comment on finite temperature correlations in integrable QFT
• Form factor expansion for thermal correlators
• Initial states in integrable quantum field theory quenches from an integral equation hierarchy
• Towards the Construction of Wightman Functions of Integrable Quantum Field Theories
• Haldane Gapped Spin Chains: Exact Low Temperature Expansions of Correlation Functions
• Mean values of local operators in highly excited Bethe states
• Finite-temperature form factors in the free Majorana theory
• Finite Temperature Dynamical Correlations in Massive Integrable Quantum Field Theories
• Finite temperature correlation functions from form factors
• Finite Temperature Dynamical Structure Factor of Alternating Heisenberg Chains
• The operator product expansion converges in perturbative field theory
• Spectral expansion for finite temperature two-point functions and clustering
• Characterization of local observables in integrable quantum field theories
• Form factor approach to diagonal finite volume matrix elements in Integrable QFT
• Form factors in equilibrium and non-equilibrium mixed states of the Ising model

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