arXiv:2412.04761 · SciPost Physics Core

Exact solution of the Izergin-Korepin Gaudin model with periodic and open boundaries

Xiaotian Xu, Pei Sun, Xin H. H. Zhang, Junpeng Cao, Tao Yang

Published May 21, 2025• 0 citations

Abstract

We study the Izergin-Korepin Gaudin models with both periodic and open integrable boundary conditions, which describe quantum systems exhibiting novel long-range interactions. Using the Bethe Ansatz approach, we derive the eigenvalues of the Gaudin operators and the corresponding Bethe Ansatz equations.

DOI: 10.21468/scipostphyscore.8.2.041

Related papers

Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms

Kun Hao, Junpeng Cao, Guang-Liang Li +3 more

arXiv:1403.7915Journal of High Energy PhysicsJun 1, 201430 citations

Exact surface energies and boundary excitations of the Izergin-Korepin model with generic boundary fields

Pengcheng Lu, Junpeng Cao, Wen‐Li Yang +2 more

A bstract The Izergin-Korepin model is an integrable model with the simplest twisted quantum affine algebra U q ( $$ {A}_2^{(2)} $$ A 2 2 ) symmetry. Applying the t - W method, we derive the homogeneous zeroes Bethe ansatz equations and the corresponding zeroes patterns of the Izergin-Korepin model with generic integrable boundaries. Based on these results, we analytically compute the surface energies and boundary excitations in different regimes of boundary parameters of the model. It is shown that in some regimes, correlation effect appears between two boundary fields.

arXiv:2407.21258Journal of High Energy PhysicsFeb 13, 20251 citation

Supersymmetrict JGaudin models and KZ equations

M. D. Gould, Yao-Zhong Zhang, Shao-you Zhao A

Supersymmetric t – J Gaudin models with open boundary conditions are investigated by means of the algebraic Bethe ansatz method. Off-shell Bethe ansatz equations of the boundary Gaudin systems are derived, and used to construct and solve the KZ equations associated with sl (2|1) (1) superalgebra.

arXiv:nlin/0202046Journal of Physics A Mathematical and GeneralOct 21, 200210 citations

The algebraic Bethe ansatz for the Izergin–Korepin model with open boundary conditions

Guang-Liang Li, Kangjie Shi, Rui‐Hong Yue

Nuclear Physics BSep 12, 200321 citations

Exact Solution of a New Class of Hubbard-Type Models with Open Boundary Conditions

Cao Li

A new class of Hubbard-type models with open boundary conditions in one dimension is studied in the frame- work of coordinate Bethe ansatz method.The energy spectrum,integrable boundary conditions and the corresponding Bethe ansatz equations are derived.

Chinese Physics CJan 1, 20070 citations

Bethe ansätze for 19-vertex models

A. Lima-Santos

The 19-vertex models of Zalomodchikov-Fateev, Izergin-Korepin and the supersymmetric with periodic boundary conditions are studied. We find the spectrum of these quantum spin chains using the coordinate Bethe ansatz. The approach is a suitable parametrization of their wavefunctions. We also applied the algebraic Bethe ansatz in order to obtain the eigenvalues and eigenvectors of the corresponding transfer matrices.

arXiv:hep-th/9807219Journal of Physics A Mathematical and GeneralJan 1, 199925 citations

arXiv:2412.04761 · SciPost Physics Core

Exact solution of the Izergin-Korepin Gaudin model with periodic and open boundaries

Xiaotian Xu, Pei Sun, Xin H. H. Zhang, Junpeng Cao, Tao Yang

Published May 21, 2025• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.21468/scipostphyscore.8.2.041

Related papers

Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms

Kun Hao, Junpeng Cao, Guang-Liang Li +3 more

The Izergin-Korepin model with general non-diagonal boundary terms, a typical integrable model beyond A-type and without U(1)-symmetry, is studied via the offdiagonal Bethe ansatz method. Based on some intrinsic properties of the R-matrix and the K-matrices, certain operator product identities of the transfer matrix are obtained at some special points of the spectral parameter. These identities and the asymptotic behaviors of the transfer matrix together allow us to construct the inhomogeneous T − Q relation and the associated Bethe ansatz equations. In the diagonal boundary limit, the reduced results coincide exactly with those obtained via other methods.The Izergin-Korepin model with general non-diagonal boundary terms, a typical integrable model beyond A-type and without U(1)-symmetry, is studied via the offdiagonal Bethe ansatz method. Based on some intrinsic properties of the R-matrix and the K-matrices, certain operator product identities of the transfer matrix are obtained at some special points of the spectral parameter. These identities and the asymptotic behaviors of the transfer matrix together allow us to construct the inhomogeneous T − Q relation and the associated Bethe ansatz equations. In the diagonal boundary limit, the reduced results coincide exactly with those obtained via other methods.

arXiv:1403.7915Journal of High Energy PhysicsJun 1, 201430 citations

Exact surface energies and boundary excitations of the Izergin-Korepin model with generic boundary fields

Pengcheng Lu, Junpeng Cao, Wen‐Li Yang +2 more

A bstract The Izergin-Korepin model is an integrable model with the simplest twisted quantum affine algebra U q ( ${A}_2^{(2)}$ A 2 2 ) symmetry. Applying the t - W method, we derive the homogeneous zeroes Bethe ansatz equations and the corresponding zeroes patterns of the Izergin-Korepin model with generic integrable boundaries. Based on these results, we analytically compute the surface energies and boundary excitations in different regimes of boundary parameters of the model. It is shown that in some regimes, correlation effect appears between two boundary fields.A bstract The Izergin-Korepin model is an integrable model with the simplest twisted quantum affine algebra U q ( $$ {A}_2^{(2)} $$ A 2 2 ) symmetry. Applying the t - W method, we derive the homogeneous zeroes Bethe ansatz equations and the corresponding zeroes patterns of the Izergin-Korepin model with generic integrable boundaries. Based on these results, we analytically compute the surface energies and boundary excitations in different regimes of boundary parameters of the model. It is shown that in some regimes, correlation effect appears between two boundary fields.

arXiv:2407.21258Journal of High Energy PhysicsFeb 13, 20251 citation

Supersymmetrict JGaudin models and KZ equations

M. D. Gould, Yao-Zhong Zhang, Shao-you Zhao A

arXiv:nlin/0202046Journal of Physics A Mathematical and GeneralOct 21, 200210 citations

The algebraic Bethe ansatz for the Izergin–Korepin model with open boundary conditions

Guang-Liang Li, Kangjie Shi, Rui‐Hong Yue

Nuclear Physics BSep 12, 200321 citations

Exact Solution of a New Class of Hubbard-Type Models with Open Boundary Conditions

Cao Li

Chinese Physics CJan 1, 20070 citations

Bethe ansätze for 19-vertex models

A. Lima-Santos

arXiv:hep-th/9807219Journal of Physics A Mathematical and GeneralJan 1, 199925 citations

A bstract The Izergin-Korepin model is an integrable model with the simplest twisted quantum affine algebra U q (

{A}_2^{(2)}

A 2 2 ) symmetry. Applying the t - W method, we derive the homogeneous zeroes Bethe ansatz equations and the corresponding zeroes patterns of the Izergin-Korepin model with generic integrable boundaries. Based on these results, we analytically compute the surface energies and boundary excitations in different regimes of boundary parameters of the model. It is shown that in some regimes, correlation effect appears between two boundary fields.