English
Related papers

Related papers: On the inhomogeneous T-Q relation for quantum inte…

200 papers

We study integrable vertex models and quantum spin chains with toroidal boundary conditions. An interesting class of such boundaries is associated with non-diagonal twist matrices. For such models there are no trivial reference states upon…

High Energy Physics - Theory · Physics 2016-09-06 C. M. Yung , M. T. Batchelor

By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the trigonometric SU(3) model with generic open boundaries. The eigenvalues of the transfer matrix are given in terms of an inhomogeneous T-Q…

Mathematical Physics · Physics 2018-06-27 Pei Sun , Zhirong Xin , Yi Qiao , Fakai Wen , Kun Hao , Junpeng Cao , Guang-Liang Li , Tao Yang , Wen-Li Yang , Kangjie Shi

We study the exact solutions of quantum integrable model associated with the $C_n$ Lie algebra, with either a periodic or an open one with off-diagonal boundary reflections, by generalizing the nested off-diagonal Bethe ansatz method.…

Mathematical Physics · Physics 2021-02-25 Guang-Liang Li , Panpan Xue , Pei Sun , Hulin Yang , Xiaotian Xu , Junpeng Cao , Tao Yang , Wen-Li Yang

We propose a set of conventional Bethe Ansatz equations and a corresponding expression for the eigenvalues of the transfer matrix for the open spin-1/2 XXZ quantum spin chain with nondiagonal boundary terms, provided that the boundary…

High Energy Physics - Theory · Physics 2008-11-26 Rafael I. Nepomechie

We study the diagonalization problem of certain discrete quantum integrable models by the method of Baxter's T-Q relation from the algebraic geometry aspect. Among those the Hofstadter type model (with the rational magnetic flux), discrete…

High Energy Physics - Theory · Physics 2009-11-07 Shao-shiung Lin , Shi-shyr Roan

Baxter's Q-operator for the quantum transfer matrix of the XXZ spin-chain is constructed employing the representation theory of quantum groups. The spectrum of this Q-operator is discussed and novel functional relations which describe the…

Mathematical Physics · Physics 2007-05-23 Christian Korff

The procedure for obtaining integrable open spin chain Hamiltonians via reflection matrices is explicitly carried out for some three-state vertex models. We have considered the 19-vertex models of Zamolodchikov-Fateev and Izergin-Korepin,…

Exactly Solvable and Integrable Systems · Physics 2014-11-18 E. C. Fireman , A. Lima-Santos , W. Utiel

The exact solution of the one-dimensional super-symmetric t-J model under generic integrable boundary conditions is obtained via the Bethe ansatz methods. With the coordinate Bethe ansatz, the corresponding R-matrix and K-matrices are…

Mathematical Physics · Physics 2015-06-18 Xin Zhang , Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

We consider the integrable open XX quantum spin chain with nondiagonal boundary terms. We derive an exact inversion identity, using which we obtain the eigenvalues of the transfer matrix and the Bethe Ansatz equations. For generic values of…

High Energy Physics - Theory · Physics 2008-11-26 Rafael I. Nepomechie

We consider the Bethe equations for the isotropic spin-1/2 Heisenberg quantum spin chain with periodic boundary conditions. We formulate a conjecture for the number of solutions with pairwise distinct roots of these equations, in terms of…

Mathematical Physics · Physics 2013-11-20 Wenrui Hao , Rafael I. Nepomechie , Andrew J. Sommese

A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the…

Strongly Correlated Electrons · Physics 2015-06-24 X. -W. Guan , A. Foerster , J. Links , H. -Q Zhou , A. Prestes Tonel , R. H. McKenzie

Baxter's Q-operator is generally believed to be the most powerful tool for the exact diagonalization of integrable models. Curiously, it has hitherto not yet been properly constructed in the simplest such system, the compact spin-1/2…

High Energy Physics - Theory · Physics 2011-03-03 Vladimir V. Bazhanov , Tomasz Lukowski , Carlo Meneghelli , Matthias Staudacher

I study the technique of Algebraic Bethe Ansatz for solving integrable models and show how it works in detail on the simplest example of spin 1/2 XXX magnetic chain. Several other models are treated more superficially, only the specific…

High Energy Physics - Theory · Physics 2007-05-23 L. D. Faddeev

The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain, of arbitrary spin-$s$, in the case, when both reflection matrices have the upper-triangular form is analyzed. The general form of the Bethe vectors is…

Exactly Solvable and Integrable Systems · Physics 2017-08-21 N. Manojlović , and I. Salom

We propose a generalization of the Baxter T-Q relation which involves more than one independent Q(u). We argue that the eigenvalues of the transfer matrix of the open XXZ quantum spin chain are given by such generalized T-Q relations, for…

High Energy Physics - Theory · Physics 2011-02-16 Rajan Murgan , Rafael I. Nepomechie

The algebraic Bethe ansatz is a powerful method to diagonalize transfer-matrices of statistical models derived from solutions of (graded) Yang Baxter equations, connected to fundamental representations of Lie (super-)algebras and their…

Condensed Matter · Physics 2009-10-31 J. Gruneberg

We consider the XXX spin-$\frac{1}{2}$ Heisenberg chain on the circle with an arbitrary twist. We characterize its spectral problem using the modified algebraic Bethe anstaz and study the scalar product between the Bethe vector and its…

Mathematical Physics · Physics 2015-12-07 Samuel Belliard , Rodrigo A. Pimenta

We obtain the Baxter Q-operators in the $U_q(\hat{sl}_2)$ invariant integrable models as a special limits of the quantum transfer matrices corresponding to different spins in the auxiliary space both from the functional relations and from…

Mathematical Physics · Physics 2015-06-23 A. A. Ovchinnikov

A quantum integrable spin chain model associated with the $G_2$ exceptional Lie algebra is studied. By using the fusion technique, the closed recursive relations among the fused transfer matrices are obtained. These identities allow us to…

Mathematical Physics · Physics 2024-12-18 Guang-Liang Li , Junpeng Cao , Pei Sun , Wen-Li Yang , Kangjie Shi , Yupeng Wang

Finding out root patterns of quantum integrable models is an important step to study their physical properties in the thermodynamic limit. Especially for models without $U(1)$ symmetry, their spectra are usually given by inhomogeneous $T-Q$…

Mathematical Physics · Physics 2021-11-12 Xiong Le , Yi Qiao , Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang