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

Journal of Physics A Mathematical and General

Finite-size corrections for nested Bethe ansatz models and conformal invariance

Hector J. de Vega

Published Dec 1, 1987• 33 citations
Publisher

Abstract

The method presented permits us to systematically compute physical magnitudes for large but finite size in theories solvable by the nested Bethe ansatz. The value of the central charge c and the surface tension are explicitly calculable in this way. For the fundamental vertex and spin models associated to simply laced Lie algebras, c turns out to be equal to the rank of the algebra.

DOI
10.1088/0305-4470/20/17/035

Related papers

Integrable vertex models and extended conformal invariance

Hector J. de Vega

Transfer matrix eigenvalues are exactly computed for large but finite size for a general class of q-state vertex models (q different states per bond, 2<or=q) from their nested Bethe ansatz equations. The conformal dimensions here obtained vary continuously as functions of the anisotropy parameter and express nicely in terms of the Cartan matrix of the underlying Lie algebra. They indicate the presence of an extended conformal invariance.

Journal of Physics A Mathematical and General•Nov 21, 1988•34 citations

A distribution approach to finite-size corrections in Bethe Ansatz solvable models

Etienne Granet, Jesper Lykke Jacobsen, Hubert Saleur

We present a new and efficient method for deriving finite-size effects in statistical physics models solvable by Bethe Ansatz. It is based on the study of the functional that maps a function to the sum of its evaluations over the Bethe roots. A simple and powerful constraint is derived when applying this functional to infinitely derivable test functions with compact support, that generalizes then to more general test functions. The method is presented in the context of the simple spin-1/2 XXZ chain for which we derive the finite-size corrections to leading eigenvalues of the Hamiltonian for any configuration of Bethe numbers with real Bethe roots. The expected results for the central charge and conformal dimensions are recovered.

arXiv:1801.05676•Nuclear Physics B•Jul 4, 2018•28 citations

Bethe-Ansatzresults for a solvable O(n) model on the square lattice

Murray T. Batchelor, Bernard Nienhuis, S. Ole Warnaar

The Bethe-Ansatz approach is used to solve a nineteen-vertex model equivalent to a spin model with O(n) symmetry on the square lattice. The bulk free energy is determined exactly on four branches of critical points. On two of these branches, the central charge is derived from finite-size corrections. On the two other branches, the nature of the Bethe Ansatz solutions prevents us from computing the central charge analytically. In this case, our approach still allows the exact numerical determination of the free energy on strips of hundreds of sites wide.

Physical Review Letters•May 22, 1989•54 citations

An analytic treatment of finite-size corrections in the spin-1 antiferromagnetic XXZ chain

Andreas Klümper, Murray T. Batchelor

It is known that the standard method for calculating finite-size corrections in Bethe ansatz solvable systems is not applicable to the Takhtajan-Babujian model and its anisotropic XXZ generalisation. The authors develop a new analytic method explicitly avoiding root densities and associated problems. Nonlinear integral equations are derived whose solutions yield the correct central charges c=1 and c=3/2 for the spin-1/2 and spin-1 XXZ chains, respectively. In the spin-1 case the authors obtain as a by-product the finite-size deviation of the Bethe ansatz roots from the 2-string formation.

Journal of Physics A Mathematical and General•Mar 7, 1990•91 citations

Conformal dimensions in Bethe ansatz solvable models

Anatoli G. Izergin, V. E. Korepin, Nicolai Reshetikhin

Models solvable by the hierarchy of Bethe ansatze (i.e. by the multicomponent Bethe ansatz) are considered. The spectrum of conformal dimensions which determines the long-distance asymptotics of correlations is calculated. This asymptotics in a general case is described by the direct sum of conformal theories, each possessing a central charge equal to one.

Journal of Physics A Mathematical and General•Jul 7, 1989•116 citations

The lowest excitations in the spin-s XXX magnet and conformal invariance

L.V. Avdeev

The Bethe-ansatz equations for the integrable spin-s isotropic Heisenberg antiferromagnet are solved numerically at a finite number of sites N. The vacuum and the lowest singlet and triplet solutions are presented for s=1/2, . . ., 2 up to sN=240. Through extrapolation of the finite-size data, the central charge and anomalous dimensions of the scaling operators for the underlying conformal field theory are calculated and found to agree with the expected theoretical values. The status of the Bethe string hypothesis about the structure of the solutions is discussed based on the obtained computer data up to s=9/2.

Journal of Physics A Mathematical and General•May 21, 1990•12 citations
The method presented permits us to systematically compute physical magnitudes for large but finite size in theories solvable by the nested Bethe ansatz. The value of the central charge c and the surface tension are explicitly calculable in this way. For the fundamental vertex and spin models associated to simply laced Lie algebras, c turns out to be equal to the rank of the algebra.
We present a new and efficient method for deriving finite-size effects in statistical physics models solvable by Bethe Ansatz. It is based on the study of the functional that maps a function to the sum of its evaluations over the Bethe roots. A simple and powerful constraint is derived when applying this functional to infinitely derivable test functions with compact support, that generalizes then to more general test functions. The method is presented in the context of the simple spin-1/2 XXZ chain for which we derive the finite-size corrections to leading eigenvalues of the Hamiltonian for any configuration of Bethe numbers with real Bethe roots. The expected results for the central charge and conformal dimensions are recovered.
The Bethe-Ansatz approach is used to solve a nineteen-vertex model equivalent to a spin model with O(n) symmetry on the square lattice. The bulk free energy is determined exactly on four branches of critical points. On two of these branches, the central charge is derived from finite-size corrections. On the two other branches, the nature of the Bethe Ansatz solutions prevents us from computing the central charge analytically. In this case, our approach still allows the exact numerical determination of the free energy on strips of hundreds of sites wide.
It is known that the standard method for calculating finite-size corrections in Bethe ansatz solvable systems is not applicable to the Takhtajan-Babujian model and its anisotropic XXZ generalisation. The authors develop a new analytic method explicitly avoiding root densities and associated problems. Nonlinear integral equations are derived whose solutions yield the correct central charges c=1 and c=3/2 for the spin-1/2 and spin-1 XXZ chains, respectively. In the spin-1 case the authors obtain as a by-product the finite-size deviation of the Bethe ansatz roots from the 2-string formation.
The Bethe-ansatz equations for the integrable spin-s isotropic Heisenberg antiferromagnet are solved numerically at a finite number of sites N. The vacuum and the lowest singlet and triplet solutions are presented for s=1/2, . . ., 2 up to sN=240. Through extrapolation of the finite-size data, the central charge and anomalous dimensions of the scaling operators for the underlying conformal field theory are calculated and found to agree with the expected theoretical values. The status of the Bethe string hypothesis about the structure of the solutions is discussed based on the obtained computer data up to s=9/2.