Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

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

Pozsgai, Balázs, István M. Szécsényi

Published Jan 1, 2018• 32 citations
OpenAlex

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 LeClairMussardo series for one-point functions, thereby satisfying the clustering requirement for the two-point function.

Related papers

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

Balázs Pozsgay, István M. Szécsényi

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:1802.05890•Journal of High Energy Physics•May 1, 2018•21 citations

The LeClair-Mussardo series and nested Bethe Ansatz

Arthur Hutsalyuk, Balázs Pozsgay, Levente Pristyák

We consider correlation functions in one dimensional quantum integrable models related to the algebra symmetries gl(2|1) and gl(3). Using the algebraic Bethe Ansatz approach we develop an expansion theorem, which leads to an infinite integral series in the thermodynamic limit. The series is the generalization of the LeClair-Mussardo series to nested Bethe Ansatz systems, and it is applicable both to one-point and two-point functions. As an example we consider the ground state density-density correlator in the Gaudin-Yang model of spin-1/2 Fermi particles. Explicit formulas are presented in a special large coupling and large imbalance limit.

arXiv:2009.13203•Nuclear Physics B•Jan 11, 2021•5 citations

Mean values of local operators in highly excited Bethe states

Balázs Pozsgay

We consider expectation values of local operators in (continuum) integrable models in a situation when the mean value is calculated in a single Bethe state with a large number of particles. We develop a form factor expansion for the thermodynamic limit of the mean value, which applies whenever the distribution of Bethe roots is given by smooth density functions. We present three applications of our general result: (i) in the framework of integrable quantum field theory (IQFT) we present a derivation of the LeClair–Mussardo formula for finite temperature one-point functions. We also extend the results to boundary operators in boundary field theories. (ii) We establish the LeClair–Mussardo formula for the non-relativistic 1D Bose gas in the framework of the algebraic Bethe ansatz (ABA). This way we obtain an alternative derivation of the results of Kormos et al for the (temperature dependent) local correlations using only the concepts of the ABA. (iii) In IQFT we consider the long-time limit of one-point functions after a certain type of global quench. It is shown that our general results imply the integral series found by Fioretti and Mussardo. We also discuss the generalized eigenstate thermalization hypothesis in the context of quantum quenches in integrable models. It is shown that a single mean value always takes the form of a thermodynamic average in a generalized Gibbs ensemble, although the relation to the conserved charges is rather indirect.

arXiv:1009.4662•Journal of Statistical Mechanics Theory and Experiment•Jan 14, 2011•101 citations

Thermodynamic bootstrap program for integrable QFT's: Form factors and correlation functions at finite energy density

Axel Cortés Cubero, Miłosz Panfil

We study the form factors of local operators of integrable QFT's between states with finite energy density. These states arise, for example, at finite temperature, or from a generalized Gibbs ensemble. We generalize Smirnov's form factor axioms, formulating them for a set of particle/hole excitations on top of the thermodynamic background, instead of the vacuum. We show that exact form factors can be found as minimal solutions of these new axioms. The thermodynamic form factors can be used to construct correlation functions on thermodynamic states. The expression found for the two-point function is similar to the conjectured LeClair-Mussardo formula, but using the new form factors dressed by the thermodynamic background, and with all singularities properly regularized. We study the different infrared asymptotics of the thermal two-point function, and show there generally exist two different regimes, manifesting massive exponential decay, or effectively gapless behavior at long distances, respectively. As an example, we compute the few-excitations form factors of vertex operators for the sinh-Gordon model.

•Jan 11, 2019•61 citations

Thermodynamic bootstrap program for integrable QFT’s: form factors and correlation functions at finite energy density

Axel Cortés Cubero, Miłosz Panfil

Abstract We study the form factors of local operators of integrable QFT’s between states with finite energy density. These states arise, for example, at finite temperature, or from a generalized Gibbs ensemble. We generalize Smirnov’s form factor axioms, formulating them for a set of particle/hole excitations on top of the thermodynamic background, instead of the vacuum. We show that exact form factors can be found as minimal solutions of these new axioms. The thermodynamic form factors can be used to construct correlation functions on thermodynamic states. The expression found for the two-point function is similar to the conjectured LeClair-Mussardo formula, but using the new form factors dressed by the thermodynamic background, and with all singularities properly regularized. We study the different infrared asymptotics of the thermal two-point function, and show there generally exist two different regimes, manifesting massive exponential decay, or effectively gapless behavior at long distances, respectively. As an example, we compute the few-excitations form factors of vertex operators for the sinh-Gordon model.

arXiv:1809.02044•Journal of High Energy Physics•Jan 1, 2019•38 citations

Spectral expansion for finite temperature two-point functions and clustering

István M. Szécsényi, G. Takács

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.

arXiv:1210.0331•Journal of Statistical Mechanics Theory and Experiment•Dec 6, 2012•25 citations
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 LeClairMussardo series for one-point functions, thereby satisfying the clustering requirement for the two-point function.
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.
We consider correlation functions in one dimensional quantum integrable models related to the algebra symmetries gl(2|1) and gl(3). Using the algebraic Bethe Ansatz approach we develop an expansion theorem, which leads to an infinite integral series in the thermodynamic limit. The series is the generalization of the LeClair-Mussardo series to nested Bethe Ansatz systems, and it is applicable both to one-point and two-point functions. As an example we consider the ground state density-density correlator in the Gaudin-Yang model of spin-1/2 Fermi particles. Explicit formulas are presented in a special large coupling and large imbalance limit.
We consider expectation values of local operators in (continuum) integrable models in a situation when the mean value is calculated in a single Bethe state with a large number of particles. We develop a form factor expansion for the thermodynamic limit of the mean value, which applies whenever the distribution of Bethe roots is given by smooth density functions. We present three applications of our general result: (i) in the framework of integrable quantum field theory (IQFT) we present a derivation of the LeClair–Mussardo formula for finite temperature one-point functions. We also extend the results to boundary operators in boundary field theories. (ii) We establish the LeClair–Mussardo formula for the non-relativistic 1D Bose gas in the framework of the algebraic Bethe ansatz (ABA). This way we obtain an alternative derivation of the results of Kormos et al for the (temperature dependent) local correlations using only the concepts of the ABA. (iii) In IQFT we consider the long-time limit of one-point functions after a certain type of global quench. It is shown that our general results imply the integral series found by Fioretti and Mussardo. We also discuss the generalized eigenstate thermalization hypothesis in the context of quantum quenches in integrable models. It is shown that a single mean value always takes the form of a thermodynamic average in a generalized Gibbs ensemble, although the relation to the conserved charges is rather indirect.
We study the form factors of local operators of integrable QFT's between states with finite energy density. These states arise, for example, at finite temperature, or from a generalized Gibbs ensemble. We generalize Smirnov's form factor axioms, formulating them for a set of particle/hole excitations on top of the thermodynamic background, instead of the vacuum. We show that exact form factors can be found as minimal solutions of these new axioms. The thermodynamic form factors can be used to construct correlation functions on thermodynamic states. The expression found for the two-point function is similar to the conjectured LeClair-Mussardo formula, but using the new form factors dressed by the thermodynamic background, and with all singularities properly regularized. We study the different infrared asymptotics of the thermal two-point function, and show there generally exist two different regimes, manifesting massive exponential decay, or effectively gapless behavior at long distances, respectively. As an example, we compute the few-excitations form factors of vertex operators for the sinh-Gordon model.
Abstract We study the form factors of local operators of integrable QFT’s between states with finite energy density. These states arise, for example, at finite temperature, or from a generalized Gibbs ensemble. We generalize Smirnov’s form factor axioms, formulating them for a set of particle/hole excitations on top of the thermodynamic background, instead of the vacuum. We show that exact form factors can be found as minimal solutions of these new axioms. The thermodynamic form factors can be used to construct correlation functions on thermodynamic states. The expression found for the two-point function is similar to the conjectured LeClair-Mussardo formula, but using the new form factors dressed by the thermodynamic background, and with all singularities properly regularized. We study the different infrared asymptotics of the thermal two-point function, and show there generally exist two different regimes, manifesting massive exponential decay, or effectively gapless behavior at long distances, respectively. As an example, we compute the few-excitations form factors of vertex operators for the sinh-Gordon model.
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.