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:1311.7692 · Journal of Statistical Mechanics Theory and Experiment

Multi-point local height probabilities of the CSOS model within the algebraic Bethe ansatz framework

D Levy-Bencheton, V. Terras

Published Apr 17, 2014• 8 citations
arXivHTMLPDF

Abstract

We study the local height probabilities of the exactly solvable cyclic solid-on-solid model within the algebraic Bethe ansatz framework. We more specifically consider multi-point local height probabilities at adjacent sites on the lattice. We derive multiple integral representations for these quantities at the thermodynamic limit, starting from finite-size expressions for the corresponding multi-point matrix elements in the Bethe basis as sums of determinants of elliptic functions.

DOI
10.1088/1742-5468/2014/04/p04014

Related papers

Multi-point local height probabilities of the CSOS model within the algebraic Bethe Ansatz framework

D Levy-Bencheton, V. Terras

We study the local height probabilities of the exactly solvable cyclic solid-on-solid model within the algebraic Bethe Ansatz framework. We more specifically consider multi-point local height probabilities at adjacent sites on the lattice. We derive multiple integral representations for these quantities at the thermodynamic limit, starting from finite-size expressions for the cor-responding multi-point matrix elements in the Bethe basis as sums of determinants of elliptic functions. 1

•Jan 1, 2013•7 citations

Spontaneous staggered polarizations of the cyclic solid-on-solid model from the algebraic Bethe Ansatz

D Levy-Bencheton, V. Terras

We compute the spontaneous staggered polarization of the cyclic SOS model at the thermodynamic limit. We use the determinant representation for finite-size form factors obtained from algebraic Bethe Ansatz.

arXiv:1304.7814•Journal of Statistical Mechanics Theory and Experiment•Oct 17, 2013•7 citations

An algebraic Bethe ansatz approach to form factors and correlation functions of the cyclic eight-vertex solid-on-solid model

D Levy-Bencheton, V. Terras

We consider the problem of the exact computation of the correlation functions of the eight-vertex solid-on-solid model by means of the algebraic Bethe ansatz. We compute the scalar product between a Bethe eigenstate and an arbitrary state of Bethe type and show that, in the cyclic case, it can be formulated as a single determinant of usual functions. It allows us to obtain determinant representations for finite-size form factors. By summing up over the form factors, we also give a multiple-integral representation for a generating function of the two-point function.

arXiv:1212.0246•Journal of Statistical Mechanics Theory and Experiment•Apr 9, 2013•20 citations

On the algebraic Bethe Ansatz approach to the correlation functions of the XXZ spin-1/2 Heisenberg chain(Solvable Lattice Models 2004 : Recent Progress on Solvable Lattice Models )

N Kitanine, Jean Michel Maillet, N. A. Slavnov +1 more

We present a review of the method we have elaborated to compute the correlation functions of the $XXZ$ spin-1/2 Heisenberg chain.This method is based on the resolution of the quantum inverse scattering problem in the algebraic Bethe Ansatz bamework, and leads to a mul- tiple integral representation of the dynamical correlation functions.We describe in particular some recent advances concerning the two-point functions: in the finite chain, they can be expressed in terms of a single multiple integral.Such a formula provides a direct analytic connection between the previously obtained multiple integral representations and the form factor expansions for the correlation functions.

数理解析研究所講究録•Apr 1, 2006•5 citations

Factorization of density matrices in the critical RSOS models

Daniel Westerfeld, Maxime Großpietsch, Hannes Kakuschke +1 more

Abstract We study reduced density matrices of the integrable critical restricted solid-on-solid (RSOS) model in a particular topological sector containing the ground state. Similar as in the spin- 1 / 2 Heisenberg model it has been observed that correlation functions of this model on short segments can be ‘factorized’: they are completely determined by a single nearest-neighbour two-point function ω and a set of structure functions. While ω captures the dependence on the system size and the state of the system the structure functions can be expressed in terms of the possible operators on the segment, in the present case representations of the Temperley–Lieb algebra TL n , and are independent of the model parameters. We present explicit results for the function ω in the infinite system ground state of the model and compute multi-point local height probabilities for up to four adjacent sites for the RSOS model and the related three-point correlation functions of non-Abelian s u ( 2 ) k anyons.

Journal of Statistical Mechanics Theory and Experiment•Aug 1, 2023•4 citations

An introduction to the algebraic Bethe ansatz

James Plunkett, Omar E. Foda

The algebraic Bethe ansatz is one of the main approaches to solving integrable models in statistical mechanics. This thesis is a detailed introduction to aspects of this technique. In chapter 1, following Takhtajan1, we fully explain all preliminaries that are required by this technique in the context of the 8-vertex model, including the solution of the Yang-Baxter equations in terms of Boltzmann weights that are parameterized by elliptic function. In chapter 2, also following Takhtajan, we restrict our attention to the special case of the 6-vertex model, with Boltzmann weights parameterized by hyperbolic trigonometric functions, formulate the model in detail on a finite lattice with periodic boundary conditions, and show how the algebraic Bethe ansatz can be used to characterize the eigenvectors and eigenvalues, in the homogeneous case (all vertical rapidities are equal, and all horizontal rapidities are also equal). In chapter 3, following Bogoliubov et al2, we consider the 6-vertex model in inhomogeneous case (all rapidities are now independenti variables) but with domain wall boundary conditions. Using the algebraic Bethe ansatz, and Izergin’s result for the partition function, we calculate boundary 1-point functions of the six-vertex model on a finite lattice and represent them in determinant form. Takhatajan, L. J. Introduction to Agebraic Bethe Ansatz, Lecture Notes in Physics, Exactly solvable problems in condensed matter and relativistic field theory 2 Boundary correlation functions of the six-vertex model J. Phys. A: Math. Gen. 35, 5525-5541 (2002)

•Jan 1, 2006•2 citations
We study the local height probabilities of the exactly solvable cyclic solid-on-solid model within the algebraic Bethe ansatz framework. We more specifically consider multi-point local height probabilities at adjacent sites on the lattice. We derive multiple integral representations for these quantities at the thermodynamic limit, starting from finite-size expressions for the corresponding multi-point matrix elements in the Bethe basis as sums of determinants of elliptic functions.
We consider the problem of the exact computation of the correlation functions of the eight-vertex solid-on-solid model by means of the algebraic Bethe ansatz. We compute the scalar product between a Bethe eigenstate and an arbitrary state of Bethe type and show that, in the cyclic case, it can be formulated as a single determinant of usual functions. It allows us to obtain determinant representations for finite-size form factors. By summing up over the form factors, we also give a multiple-integral representation for a generating function of the two-point function.
We present a review of the method we have elaborated to compute the correlation functions of the XXZXXZXXZ spin-1/2 Heisenberg chain.This method is based on the resolution of the quantum inverse scattering problem in the algebraic Bethe Ansatz bamework, and leads to a mul- tiple integral representation of the dynamical correlation functions.We describe in particular some recent advances concerning the two-point functions: in the finite chain, they can be expressed in terms of a single multiple integral.Such a formula provides a direct analytic connection between the previously obtained multiple integral representations and the form factor expansions for the correlation functions.
Abstract We study reduced density matrices of the integrable critical restricted solid-on-solid (RSOS) model in a particular topological sector containing the ground state. Similar as in the spin- 1 / 2 Heisenberg model it has been observed that correlation functions of this model on short segments can be ‘factorized’: they are completely determined by a single nearest-neighbour two-point function ω and a set of structure functions. While ω captures the dependence on the system size and the state of the system the structure functions can be expressed in terms of the possible operators on the segment, in the present case representations of the Temperley–Lieb algebra TL n , and are independent of the model parameters. We present explicit results for the function ω in the infinite system ground state of the model and compute multi-point local height probabilities for up to four adjacent sites for the RSOS model and the related three-point correlation functions of non-Abelian s u ( 2 ) k anyons.
The algebraic Bethe ansatz is one of the main approaches to solving integrable models in statistical mechanics. This thesis is a detailed introduction to aspects of this technique. In chapter 1, following Takhtajan1, we fully explain all preliminaries that are required by this technique in the context of the 8-vertex model, including the solution of the Yang-Baxter equations in terms of Boltzmann weights that are parameterized by elliptic function. In chapter 2, also following Takhtajan, we restrict our attention to the special case of the 6-vertex model, with Boltzmann weights parameterized by hyperbolic trigonometric functions, formulate the model in detail on a finite lattice with periodic boundary conditions, and show how the algebraic Bethe ansatz can be used to characterize the eigenvectors and eigenvalues, in the homogeneous case (all vertical rapidities are equal, and all horizontal rapidities are also equal). In chapter 3, following Bogoliubov et al2, we consider the 6-vertex model in inhomogeneous case (all rapidities are now independenti variables) but with domain wall boundary conditions. Using the algebraic Bethe ansatz, and Izergin’s result for the partition function, we calculate boundary 1-point functions of the six-vertex model on a finite lattice and represent them in determinant form. Takhatajan, L. J. Introduction to Agebraic Bethe Ansatz, Lecture Notes in Physics, Exactly solvable problems in condensed matter and relativistic field theory 2 Boundary correlation functions of the six-vertex model J. Phys. A: Math. Gen. 35, 5525-5541 (2002)