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:2409.05309

The emptiness formation probability, and representations for nonlocal correlation functions, of the 20-vertex model

Pete Rigas

Published Sep 9, 2024• 0 citations
arXivHTMLPDF

Abstract

We study the emptiness formation probability, along with various representations for nonlocal correlation functions, of the 20-vertex model. In doing so, we leverage previous arguments for representations of nonlocal correlation functions for the 6-vertex model, under domain-wall boundary conditions, due to Colomo, Di Giulio, and Pronko, in addition to the inhomogeneous, and homogeneous, determinantal representations for the 20-vertex partition function due to Di Francesco, also under domain-wall boundary conditions. By taking a product of row configuration probabilities, we obtain a desired contour integral representation for nonlocal correlations from a determinantal representation. Finally, a counterpart of the emptiness formation probability is introduced for the 20-vertex model.

DOI
10.48550/arxiv.2409.05309

Related papers

Six-vertex model on a finite lattice: Integral representations for nonlocal correlation functions

Filippo Colomo, Giuseppe Di Giulio, A. G. Pronko

We consider the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions. To this aim, we formulate the model as a scalar product of off-shell Bethe states, and, by applying the quantum inverse scattering method, we derive three different integral representations for these states. By suitably combining such representations, and using certain antisymmetrization relation in two sets of variables, it is possible to derive integral representations for various correlation functions. In particular, focusing on the emptiness formation probability, besides reproducing the known result, obtained by other means elsewhere, we provide a new one. By construction, the two representations differ in the number of integrations and their equivalence is related to a hierarchy of highly nontrivial identities.

arXiv:2107.13358•Nuclear Physics B•Sep 15, 2021•10 citations

Six-vertex model with domain wall boundary conditions: variable inhomogeneities

Jan de Gier, V Korepin

We consider the six-vertex model with domain wall boundary conditions. We choose the inhomogeneities as solutions of the Bethe Ansatz equations. These equations have many solutions, so we can consider a wide variety of inhomogeneities. For certain choices of the inhomogeneities we study arrow correlation functions on the horizontal line going through the centre. In particular, we obtain a multiple integral representation for the emptiness formation probability that generalizes the known formulae for XXZ antiferromagnets.

arXiv:math-ph/0101036•Journal of Physics A Mathematical and General•Sep 21, 2001•5 citations

Six-Vertex Model with Domain wall boundary conditions. Variable Inhomogeneities

Jan de Gier, V. E. Korepin

We consider the six-vertex model with domain wall boundary conditions. We choose the inhomogeneities as solutions of the Bethe Ansatz equations. The Bethe Ansatz equations have many solutions, so we can consider a wide variety of inhomogeneities. For certain choices of the inhomogeneities we study arrow correlation functions on the horizontal line going through the centre. In particular we obtain a multiple integral representation for the emptiness formation probability that generalizes the known formulæ for XXZ antiferromagnets. 1

•Jan 1, 2001•7 citations

Boundary correlations for the six-vertex model with reflecting end boundary condition

I R Passos, G A P Ribeiro

Abstract We consider the six-vertex model with reflecting end boundary condition. We compute analytically boundary correlation functions, such as the boundary polarization and the emptiness formation probability. In order to do that, we use the Sklyanin’s reflection algebra to derive recursion relations for the partition function of the model as well as for the boundary correlations in terms of the partition function. Thanks to the Tsuchiya determinant formula, these recursion relations allow the boundary correlations to be also efficiently written in determinant form.

arXiv:1904.06383•Journal of Statistical Mechanics Theory and Experiment•Aug 1, 2019•2 citations

Factorization of rational six vertex model partition functions

Kohei Motegi

We show factorization formulas for a class of partition functions of rational six vertex model. First we show factorization formulas for partition functions under triangular boundary. Further, by combining the factorization formulas with the explicit forms of the generalized domain wall boundary partition functions by Belliard-Pimenta-Slavnov, we derive factorization formulas for partition functions under trapezoid boundary which can be viewed as a generalization of triangular boundary. We also discuss an application to emptiness formation probabilities under trapezoid boundary which admit determinant representations.

arXiv:2410.03153•Nuclear Physics B•Nov 17, 2024•0 citations

On the spin–spin correlation functions of the XXZ spin- infinite chain

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

We obtain a new multiple integral representation for the spin–spin correlation functions of the XXZ spin- infinite chain. We show that this representation is closely related with the partition function of the six-vertex model with domain wall boundary conditions.

arXiv:hep-th/0407223•Journal of Physics A Mathematical and General•Aug 10, 2005•25 citations
We study the emptiness formation probability, along with various representations for nonlocal correlation functions, of the 20-vertex model. In doing so, we leverage previous arguments for representations of nonlocal correlation functions for the 6-vertex model, under domain-wall boundary conditions, due to Colomo, Di Giulio, and Pronko, in addition to the inhomogeneous, and homogeneous, determinantal representations for the 20-vertex partition function due to Di Francesco, also under domain-wall boundary conditions. By taking a product of row configuration probabilities, we obtain a desired contour integral representation for nonlocal correlations from a determinantal representation. Finally, a counterpart of the emptiness formation probability is introduced for the 20-vertex model.
We consider the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions. To this aim, we formulate the model as a scalar product of off-shell Bethe states, and, by applying the quantum inverse scattering method, we derive three different integral representations for these states. By suitably combining such representations, and using certain antisymmetrization relation in two sets of variables, it is possible to derive integral representations for various correlation functions. In particular, focusing on the emptiness formation probability, besides reproducing the known result, obtained by other means elsewhere, we provide a new one. By construction, the two representations differ in the number of integrations and their equivalence is related to a hierarchy of highly nontrivial identities.
We consider the six-vertex model with domain wall boundary conditions. We choose the inhomogeneities as solutions of the Bethe Ansatz equations. These equations have many solutions, so we can consider a wide variety of inhomogeneities. For certain choices of the inhomogeneities we study arrow correlation functions on the horizontal line going through the centre. In particular, we obtain a multiple integral representation for the emptiness formation probability that generalizes the known formulae for XXZ antiferromagnets.
We consider the six-vertex model with domain wall boundary conditions. We choose the inhomogeneities as solutions of the Bethe Ansatz equations. The Bethe Ansatz equations have many solutions, so we can consider a wide variety of inhomogeneities. For certain choices of the inhomogeneities we study arrow correlation functions on the horizontal line going through the centre. In particular we obtain a multiple integral representation for the emptiness formation probability that generalizes the known formulæ for XXZ antiferromagnets. 1
Abstract We consider the six-vertex model with reflecting end boundary condition. We compute analytically boundary correlation functions, such as the boundary polarization and the emptiness formation probability. In order to do that, we use the Sklyanin’s reflection algebra to derive recursion relations for the partition function of the model as well as for the boundary correlations in terms of the partition function. Thanks to the Tsuchiya determinant formula, these recursion relations allow the boundary correlations to be also efficiently written in determinant form.
We show factorization formulas for a class of partition functions of rational six vertex model. First we show factorization formulas for partition functions under triangular boundary. Further, by combining the factorization formulas with the explicit forms of the generalized domain wall boundary partition functions by Belliard-Pimenta-Slavnov, we derive factorization formulas for partition functions under trapezoid boundary which can be viewed as a generalization of triangular boundary. We also discuss an application to emptiness formation probabilities under trapezoid boundary which admit determinant representations.