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/0001172

Finite Volume Spectrum of Sine-Gordon Model and its Restrictions

Giovanni Feverati

Published Jan 26, 2000• 19 citations
arXivHTMLPDF

Abstract

In this thesis, we review recent progresses on Nonlinear Integral Equation approach to finite size effects in two dimensional integrable quantum field theories, with emphasis to Sine-Gordon/Massive Thirring model and restrictions to minimal models perturbed by $Φ_{1,3}$. Exact calculations of the dependence of energy levels on the size are presented for vacuum and many excited states.

DOI
10.48550/arxiv.hep-th/0001172

Related papers

Finite size effects in integrable quantum field theory: the sine-Gordon model with boundaries

Marco Bellacosa

In this thesis we review recent progresses on Nonlinear Integral Equation approach to finite size effects in two dimensional integrable quantum field theory with boundaries, with emphasis to sine-Gordon model with Dirichlet boundary conditions. Exact calculations of the dependence of the energy spectrum on the size and on boundary conditions are presented for vacuum and many excited states.

arXiv:hep-th/0406032•Jun 3, 2004•0 citations

Perturbed conformal field theory, nonlinear integral equations and spectral problems

Clare Dunning

This thesis is concerned with various aspects of perturbed conformal field theory and the methods used to calculate finite-size effects of integrable quantum field theories. Nonlinear integral equations are the main tools to find the exact ground-state energy of a quantum field theory. The thermodyamic Bethe ansatz (TBA) equations are a set of examples and are known for a large number of models. However, it is also an interesting question to find exact equations describing the excited states of integrable models. The first part of this thesis uses analytical continuation in a continuous parameter to find TBA like equations describing the spin-zero excited states of the sine-Gordon model at coupling β(^2) = 16π/3. Comparisons are then made with a further type of nonlinear integral equation which also predicts the excited state energies. Relations between the two types of equation are studied using a set of functional relations recently introduced in integrable quantum field theory. A relevant perturbation of a conformal field theory results in either a massive quantum field theory such as the sine-Gordon model, or a different massless conformal field theory. The second part of this thesis investigates flows between conformal field theories using a nonlinear integral equation. New families of flows are found which exhibit a rather unexpected behaviour. The final part of this thesis begins with a review of a connection between integrable quantum field theory and properties of certain ordinary differential equations of second- and third-order. The connection is based on functional relations which appear on both sides of the correspondence; for the second-order case these are exactly the functional relations mentioned above. The results are extended to include a correspondence between n(^th) order differential equations and Bethe ansatz system of SU(n) type. A set of nonlinear integral equations are derived to check the results.

•Jan 1, 2000•2 citations

FINITE SIZE EFFECTS IN INTEGRABLE QUANTUM FIELD THEORIES

Francesco Ravanini

The study of Finite Size Effects in Quantum Field Theory allows the extraction of precious perturbative and non-perturbative information. The use of scaling functions can connect the particle content (scattering theory formulation) of a QFT to its ultraviolet Conformal Field Theory content. If the model is integrable, a method of investigation through a nonlinear integral equation equivalent to Bethe Ansatz and deducible from a light-cone lattice regularization is available. It allows to reconstruct the S-matrix and to understand the locality properties in terms of Bethe root configurations, thanks to the link to ultraviolet CFT guaranteed by the exact determination of scaling function. This method is illustrated in practice for Sine-Gordon / massive Thirring models, clarifying their locality structure and the issues of equivalence between the two models. By restriction of the Sine-Gordon model it is also possible to control the scaling functions of minimal models perturbed by Phi_1,3

arXiv:hep-th/0102148•Non-Perturbative QFT Methods and Their Applications•May 1, 2001•9 citations

Wave functions and finite size effects in a two-dimensional lattice field theory

H. B. Thacker

A study of finite size corrections to the masses of fermions and bound states in the Baxter/massive Thirring/sine Gordon lattice field theory is discussed. It is shown that information on bound tate wave functions may be used to extrapolate Monte Carlo mass calculations to infinite volume. 10 refs., 4 figs.

•Jun 1, 1985•0 citations

Quantum field ground state of the sine-Gordon model with finite soliton density: exact results

F. D. M. Haldane

The Bethe ansatz solutions of the massive Thirring model are renormalised and used to obtain exactly the ground-state properties of the sine-Gordon model with a finite density of topological solitons. Using a theory of 1D quantum fluids, the correlation function exponents and low-energy excitation spectrum are obtained. Expansions in various limits are given, and various crossovers described.

Journal of Physics A Mathematical and General•Feb 1, 1982•55 citations

Commensurate-Incommensurate Transition in the Two-Dimensional Sine-Gordon System: the Bethe Ansatz Calculation

Yukio Okwamoto

Recently Haldane has derived the Bethe ansatz equations describing the ground state properties of the massive Thirring model with finite `hole' density (the quantum sine-Gordon model with finite soliton density). His derivation is explicitly confirmed here using a particular cutoff scheme, and his solutions of the equations in various limits are reviewed with complementary results. The commensurate-incommensurate transition in the two-dimensional sine-Gordon model with a uniaxial misfit is examined at finite temperatures using the results obtained in the massive Thirring model.

Journal of the Physical Society of Japan•Mar 1, 1983•6 citations
In this thesis, we review recent progresses on Nonlinear Integral Equation approach to finite size effects in two dimensional integrable quantum field theories, with emphasis to Sine-Gordon/Massive Thirring model and restrictions to minimal models perturbed by Φ1,3Φ_{1,3}Φ1,3​. Exact calculations of the dependence of energy levels on the size are presented for vacuum and many excited states.
This thesis is concerned with various aspects of perturbed conformal field theory and the methods used to calculate finite-size effects of integrable quantum field theories. Nonlinear integral equations are the main tools to find the exact ground-state energy of a quantum field theory. The thermodyamic Bethe ansatz (TBA) equations are a set of examples and are known for a large number of models. However, it is also an interesting question to find exact equations describing the excited states of integrable models. The first part of this thesis uses analytical continuation in a continuous parameter to find TBA like equations describing the spin-zero excited states of the sine-Gordon model at coupling β(^2) = 16π/3. Comparisons are then made with a further type of nonlinear integral equation which also predicts the excited state energies. Relations between the two types of equation are studied using a set of functional relations recently introduced in integrable quantum field theory. A relevant perturbation of a conformal field theory results in either a massive quantum field theory such as the sine-Gordon model, or a different massless conformal field theory. The second part of this thesis investigates flows between conformal field theories using a nonlinear integral equation. New families of flows are found which exhibit a rather unexpected behaviour. The final part of this thesis begins with a review of a connection between integrable quantum field theory and properties of certain ordinary differential equations of second- and third-order. The connection is based on functional relations which appear on both sides of the correspondence; for the second-order case these are exactly the functional relations mentioned above. The results are extended to include a correspondence between n(^th) order differential equations and Bethe ansatz system of SU(n) type. A set of nonlinear integral equations are derived to check the results.
The study of Finite Size Effects in Quantum Field Theory allows the extraction of precious perturbative and non-perturbative information. The use of scaling functions can connect the particle content (scattering theory formulation) of a QFT to its ultraviolet Conformal Field Theory content. If the model is integrable, a method of investigation through a nonlinear integral equation equivalent to Bethe Ansatz and deducible from a light-cone lattice regularization is available. It allows to reconstruct the S-matrix and to understand the locality properties in terms of Bethe root configurations, thanks to the link to ultraviolet CFT guaranteed by the exact determination of scaling function. This method is illustrated in practice for Sine-Gordon / massive Thirring models, clarifying their locality structure and the issues of equivalence between the two models. By restriction of the Sine-Gordon model it is also possible to control the scaling functions of minimal models perturbed by Phi_1,3
Recently Haldane has derived the Bethe ansatz equations describing the ground state properties of the massive Thirring model with finite `hole' density (the quantum sine-Gordon model with finite soliton density). His derivation is explicitly confirmed here using a particular cutoff scheme, and his solutions of the equations in various limits are reviewed with complementary results. The commensurate-incommensurate transition in the two-dimensional sine-Gordon model with a uniaxial misfit is examined at finite temperatures using the results obtained in the massive Thirring model.