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Finite size matrix elements and thermal correlators in integrable quantum field theories

István M. Szécsényi

Jan 1, 20170 citations

Bethe ansatz matrix elements as non-relativistic limits of form factors of quantum field theory

Márton Kormos, Giuseppe Mussardo, Balázs Pozsgay

We show that the matrix elements of integrable models computed by the Algebraic Bethe Ansatz can be put in direct correspondence with the Form Factors of integrable relativistic field theories. This happens when the S-matrix of a Bethe Ansatz model can be regarded as a suitable non-relativistic limit of the S-matrix of a field theory, and when there is a well-defined mapping between the Hilbert spaces and operators of the two theories. This correspondence provides an efficient method to compute matrix elements of Bethe Ansatz integrable models, overpassing the technical difficulties of their direct determination. We analyze this correspondence for the simplest example in which it occurs, i.e. the Quantum Non-Linear Schrodinger and the Sinh-Gordon models.We show that the matrix elements of integrable models computed by the Algebraic Bethe Ansatz can be put in direct correspondence with the Form Factors of integrable relativistic field theories. This happens when the S-matrix of a Bethe Ansatz model can be regarded as a suitable non-relativistic limit of the S-matrix of a field theory, and when there is a well-defined mapping between the Hilbert spaces and operators of the two theories. This correspondence provides an efficient method to compute matrix elements of Bethe Ansatz integrable models, overpassing the technical difficulties of their direct determination. We analyze this correspondence for the simplest example in which it occurs, i.e. the Quantum Non-Linear Schrodinger and the Sinh-Gordon models.

arXiv:1002.3387Journal of Statistical Mechanics Theory and ExperimentMay 20, 201026 citations

Field operators and their spectral properties in finite-dimensional quantum field theory

Vladimir Naroditsky

Foundations of PhysicsMar 1, 19850 citations

Completing the Bootstrap Program for TT-Deformed Massive Integrable Quantum Field Theories

Fabio Sailis

This thesis addresses the problem of extending the Form Factor Bootstrap Program (FFBP), the main tool for computing correlation functions in integrable quantum field theories (IQFTs), to the case of irrelevant deformations, with particular focus on generalised TT-deformations. Such models pose new challenges, including the emergence of a minimal length scale and the loss of strict locality. Relying solely on the exact S-matrix, we construct the minimal form factors of TT-deformed theories and analyze their properties in detail. This resolves longstanding ambiguities in previous constructions and leads to a deeper understanding of both deformed and standard IQFTs.This thesis addresses the problem of extending the Form Factor Bootstrap Program (FFBP), the main tool for computing correlation functions in integrable quantum field theories (IQFTs), to the case of irrelevant deformations, with particular focus on generalised TT-deformations. Such models pose new challenges, including the emergence of a minimal length scale and the loss of strict locality. Relying solely on the exact S-matrix, we construct the minimal form factors of TT-deformed theories and analyze their properties in detail. This resolves longstanding ambiguities in previous constructions and leads to a deeper understanding of both deformed and standard IQFTs.

Jan 1, 20260 citations

Integrable quantum field theory with boundary

Alexander B. Zamolodchikov

Jan 1, 19940 citations

Replica-deformation of the SU(2)-invariant Thirring model via solutions of the qKZ equation

Mathias Pillin

Dedicated to the memory of Moshé Flato The response of an integrable QFT under variation of the Unruh temperature has recently been shown to be computable from an S-matrix preserving (“replica”) deformation of the form factor approach. We show that replicadeformed form factors of the SU(2)-invariant Thirring model can be found among the solutions of the rational sl2-type quantum Knizhnik-Zamolodchikov equation at generic level. We show that modulo conserved charge solutions the deformed form factors are in one-to-one correspondence to the ones at level zero and use this to conjecture the deformed form factors of the Noether The form factor approach to massive integrable quantum field theories (QFTs) [9, 20] provides a powerful tool to compute exact matrix elements of local operators from the knowledge of the (factorized) S-matrix. To be precise, a form factor in this context is the matrix element of some local operator between the physical vacuum and a multi-particleDedicated to the memory of Moshé Flato The response of an integrable QFT under variation of the Unruh temperature has recently been shown to be computable from an S-matrix preserving (“replica”) deformation of the form factor approach. We show that replicadeformed form factors of the SU(2)-invariant Thirring model can be found among the solutions of the rational sl2-type quantum Knizhnik-Zamolodchikov equation at generic level. We show that modulo conserved charge solutions the deformed form factors are in one-to-one correspondence to the ones at level zero and use this to conjecture the deformed form factors of the Noether The form factor approach to massive integrable quantum field theories (QFTs) [9, 20] provides a powerful tool to compute exact matrix elements of local operators from the knowledge of the (factorized) S-matrix. To be precise, a form factor in this context is the matrix element of some local operator between the physical vacuum and a multi-particle

Jan 1, 19992 citations

Matrix elements of the operator TT¯ in integrable quantum field theory

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