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

arXiv:hep-th/9801046 · Journal of Physics A Mathematical and General

The determinant representation for quantum correlation functions of the sinh-Gordon model

V. E. Korepin, N. A. Slavnov

Published Nov 20, 1998• 19 citations
arXivHTMLPDF

Abstract

We consider the quantum sinh-Gordon model in this paper. Form factors in this model were calculated by Mussardo and colleagues. We sum up all contributions of form factors and obtain a closed expression for a correlation function. This expression is a determinant of an integral operator. Similar determinant representations have been proven to be useful not only in the theory of correlation functions, but also in matrix models.

DOI
10.1088/0305-4470/31/46/018

Related papers

A determinant representation for a correlation function of the scaling Lee - Yang model

V. E. Korepin, Takeshi Oota

We consider the scaling Lee - Yang model. It corresponds to the unique perturbation of the minimal CFT model . This model is not unitary. We are using an expression for form factors in terms of symmetric polynomials in order to obtain a closed expression for the correlation function of the trace of the energy-momentum tensor. This expression is a determinant of an integral operator. Similar determinant representations were proven to be useful not only for quantum correlation functions but also in matrix models.

arXiv:hep-th/9802003•Journal of Physics A Mathematical and General•May 15, 1998•8 citations

Algebraic approach to form factors in the complex sinh-Gordon theory

Michael Lashkevich, Yaroslav Pugai

We study form factors of the quantum complex sinh-Gordon theory in the algebraic approach. In the case of exponential fields the form factors can be obtained from the known form factors of the ZN-symmetric Ising model. The algebraic construction also provides an Ansatz for form factors of descendant operators. We obtain generating functions of such form factors and establish their main properties: the cluster factorization and reflection equations.

arXiv:1610.04926•Physics Letters B•Nov 22, 2016•1 citation

A note on four-particle form factors of operators T 2 n T − 2 n in the sinh-Gordon model

Michael Lashkevich, Yaroslav Pugai

Abstract The diagonal matrix elements 〈 θ 1 , θ 2 ∣ T 2 n T − 2 n ∣ θ 1 , θ 2 〉 between two-particle states in the sinh-Gordon model are computed analytically for all integers n > 0 . This confirms the proposal [1] by Smirnov and Zamolodchikov for these matrix elements and demonstrates the effectiveness of the algebraic approach to form factors.

arXiv:1602.05735•Journal of Physics A Mathematical and Theoretical•Jun 24, 2016•5 citations

On the form factors of local operators in the lattice sine–Gordon model

Nicolas Grosjean, Jean Michel Maillet, Giuliano Niccoli

We develop a method for computing form factors of local operators in the framework of Sklyanin's separation of variables (SOV) approach to quantum integrable systems.For that purpose, we consider the sine-Gordon model on a finite lattice and in finite dimensional cyclic representations as our main example.We first build our two central tools for computing matrix elements of local operators, namely, a generic determinant formula for the scalar products of states in the SOV framework and the reconstruction of local fields in terms of the separate variables.The general form factors are then obtained as sums of determinants of finite dimensional matrices, their matrix elements being given as weighted sums running over the separate variables and involving the Baxter Q-operator eigenvalues.

arXiv:1204.6307•Journal of Statistical Mechanics Theory and Experiment•Oct 10, 2012•51 citations

Determinant Representations of Correlation Functions for the Supersymmetric t-J Model

Shao-you Zhao A, Wen‐Li Yang, Yao-Zhong Zhang

Working in the F-basis provided by the factorizing F-matrix, the scalar products of Bethe states for the supersymmetric t-J model are represented by determinants. By means of these results, we obtain determinant representations of correlation functions The computation of correlation functions is one of the major challenging problems in the theory of quantum integrable models [1, 2]. There are currently two approaches for computing the correlation functions of a quantum integrable model. One is the vertex operator method (see e.g. [3-8]), and another one is based on the detailed analysis of the structure of

•Jan 1, 2005•17 citations

On the Construction of Correlation Functions for the Integrable Supersymmetric Fermion Models

Shao-you Zhao A, Wen‐Li Yang, Yao-Zhong Zhang

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing $F$-matrices (or the so-called $F$-basis) play an important role in the construction. In the $F$-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the $\\gl$ (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analysing physical properties of the integrable models in the thermodynamical limit.

•Jan 11, 2006•7 citations
We consider the quantum sinh-Gordon model in this paper. Form factors in this model were calculated by Mussardo and colleagues. We sum up all contributions of form factors and obtain a closed expression for a correlation function. This expression is a determinant of an integral operator. Similar determinant representations have been proven to be useful not only in the theory of correlation functions, but also in matrix models.
We consider the scaling Lee - Yang model. It corresponds to the unique perturbation of the minimal CFT model . This model is not unitary. We are using an expression for form factors in terms of symmetric polynomials in order to obtain a closed expression for the correlation function of the trace of the energy-momentum tensor. This expression is a determinant of an integral operator. Similar determinant representations were proven to be useful not only for quantum correlation functions but also in matrix models.
We develop a method for computing form factors of local operators in the framework of Sklyanin's separation of variables (SOV) approach to quantum integrable systems.For that purpose, we consider the sine-Gordon model on a finite lattice and in finite dimensional cyclic representations as our main example.We first build our two central tools for computing matrix elements of local operators, namely, a generic determinant formula for the scalar products of states in the SOV framework and the reconstruction of local fields in terms of the separate variables.The general form factors are then obtained as sums of determinants of finite dimensional matrices, their matrix elements being given as weighted sums running over the separate variables and involving the Baxter Q-operator eigenvalues.
Working in the F-basis provided by the factorizing F-matrix, the scalar products of Bethe states for the supersymmetric t-J model are represented by determinants. By means of these results, we obtain determinant representations of correlation functions The computation of correlation functions is one of the major challenging problems in the theory of quantum integrable models [1, 2]. There are currently two approaches for computing the correlation functions of a quantum integrable model. One is the vertex operator method (see e.g. [3-8]), and another one is based on the detailed analysis of the structure of
We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing FFF-matrices (or the so-called FFF-basis) play an important role in the construction. In the FFF-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the gl\\glgl (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analysing physical properties of the integrable models in the thermodynamical limit.