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Related papers: Algebraic Bethe ansatz for singular solutions

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We analyze the ground state of the open spin-1/2 isotropic quantum spin chain with a non-diagonal boundary term using a recently proposed Bethe ansatz solution. As the coefficient of the non-diagonal boundary term tends to zero, the Bethe…

Mathematical Physics · Physics 2015-06-17 Rafael I. Nepomechie , Chunguang Wang

The integrable close and open chain models can be formulated in terms of generators of the Hecke algebras. In this review paper, we describe in detail the Bethe ansatz for the XXX and the XXZ integrable close chain models. We find the Bethe…

Mathematical Physics · Physics 2015-07-02 C. Burdik , J. Fuksa , A. P. Isaev , S. O. Krivonos , O. Navratil

We present a numerical approach which allows the solving of Bethe equations whose solutions define the eigenstates of Gaudin models. By focusing on a new set of variables, the canceling divergences which occur for certain values of the…

Mesoscale and Nanoscale Physics · Physics 2011-06-15 Alexandre Faribault , Omar El Araby , Christoph Sträter , Vladimir Gritsev

In this paper we investigate complex solutions of the Bethe equations in the two-particle sector both for arbitrary finite number of sites and for the thermodynamic limit . We find the number of complex solutions (strings) and compare it…

High Energy Physics - Theory · Physics 2014-11-18 A. Ilakovac , M. Kolanovic , S. Pallua , P. Prester

We describe a method to derive, from first principles, the long-distance asymptotic behavior of correlation functions of integrable models in the framework of the algebraic Bethe ansatz. We apply this approach to the longitudinal spin- spin…

Mathematical Physics · Physics 2009-09-25 N. Kitanine , K. K. Kozlowski , J. M. Maillet , N. A. Slavnov , V. Terras

We propose a Bethe-Ansatz-type solution of the open spin-1/2 integrable XXZ quantum spin chain with general integrable boundary terms and bulk anisotropy values i \pi/(p+1), where p is a positive integer. All six boundary parameters are…

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

The Bethe Ansatz is a method that is used in quantum integrable models in order to solve them explicitly. This method is explained here in a general framework, which applies to 1D quantum spin chains, 2D statistical lattice models (vertex…

solv-int · Physics 2007-05-23 P. Zinn-Justin

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

The Nested Bethe Ansatz is generalized to open boundary conditions. This is used to find the exact eigenvectors and eigenvalues of the $A_{n-1}$ vertex model with fixed open boundary conditions and the corresponding $SU_{q}(n)$ invariant…

High Energy Physics - Theory · Physics 2009-10-22 H. J. de Vega , A. González--Ruiz

We express $D^{(2)}_{2}$ transfer matrices as products of $A^{(1)}_{1}$ transfer matrices, for both closed and open spin chains. We use these relations, which we call factorization identities, to solve the models by algebraic Bethe ansatz.…

High Energy Physics - Theory · Physics 2021-01-20 Rafael I. Nepomechie , Ana L. Retore

We diagonalize Q-operators for rational homogeneous sl(2)-invariant Heisenberg spin chains using the algebraic Bethe ansatz. After deriving the fundamental commutation relations relevant for this case from the Yang-Baxter equation we…

Mathematical Physics · Physics 2017-11-28 Rouven Frassek

We review recent results on the Bethe Ansatz solutions for the eigenvalues of the transfer matrix of an integrable open XXZ quantum spin chain using functional relations which the transfer matrix obeys at roots of unity. First, we consider…

High Energy Physics - Theory · Physics 2008-11-26 Rajan Murgan

We derive exactly the number of complex solutions with two down-spins in the massive regime of the periodic spin-1/2 XXZ spin chain of $N$ sites. Here we remark that every solution of the Bethe ansatz equations is characterized by a set of…

Statistical Mechanics · Physics 2019-05-22 Takashi Imoto , Jun Sato , Tetsuo Deguchi

We present a procedure to extract the generalised eigenvectors of a non-diagonalisable matrix by considering a diagonalisable perturbation of it and computing the non-diagonalisable limit of its eigenvectors. As an example of this process,…

High Energy Physics - Theory · Physics 2022-07-13 Juan Miguel Nieto García , Leander Wyss

The transfer matrix of the general integrable open XXZ quantum spin chain obeys certain functional relations at roots of unity. By exploiting these functional relations, we determine the Bethe Ansatz solution for the transfer matrix…

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

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

In this paper, we show the integrability of spin-1/2 XXZ Heisenberg chain with two arbitrary spin boundary Impurities. By using the fusion method, we generalize it to the spin-1 XXZ chain. Then the eigenvalues of Hamiltonians of these…

Condensed Matter · Physics 2009-10-31 Boyu Hou , Kangjie Shi , Ruihong Yue , Shaoyou Zhao

As part of a study that investigates the dynamics of the s=1/2 XXZ model in the planar regime |Delta|<1, we discuss the singular nature of the Bethe ansatz equations for the case Delta=0 (XX model). We identify the general structure of the…

Strongly Correlated Electrons · Physics 2009-11-10 Daniel Biegel , Michael Karbach , Gerhard Muller , Klaus Wiele

The nested off-diagonal Bethe ansatz method is proposed to diagonalize multi-component integrable models with generic integrable boundaries. As an example, the exact solutions of the su(n)-invariant spin chain model with both periodic and…

High Energy Physics - Theory · Physics 2015-06-18 Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

I derived Bethe Ansatz equations for two model Periodic Quantum Circuits: 1) XXZ model; 2) Chiral Hubbard Model. I obtained explicit expressions for the spectra of the strings of any length. These analytic results may be useful for…

Mesoscale and Nanoscale Physics · Physics 2021-07-14 I. L. Aleiner