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We consider general cyclic representations of the 6-vertex Yang-Baxter algebra and analyze the associated quantum integrable systems, the Bazhanov-Stroganov model and the corresponding chiral Potts model on finite size lattices. We first…

Mathematical Physics · Physics 2017-03-17 N. Grosjean , J. M. Maillet , G. Niccoli

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

We construct symmetric and exterior powers of the vector representation of the elliptic quantum groups $E_{\tau,\eta}(gl_N)$. The corresponding transfer matrices give rise to various integrable difference equations which could be solved in…

q-alg · Mathematics 2009-10-30 Giovanni Felder , Alexander Varchenko

The nested off-diagonal Bethe ansatz is generalized to study the quantum spin chain associated with the $SU_q(3)$ R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator…

Mathematical Physics · Physics 2016-08-24 Guang-Liang Li , Junpeng Cao , Kun Hao , Fakai Wen , Wen-Li Yang , Kangjie Shi

This paper is concerned with the study of properties of the exact solution of the fundamental integrable $G_2$ vertex model. The model $R$-matrix and respective spin chain are presented in terms of the basis generators of the $G_2$ Lie…

Mathematical Physics · Physics 2023-03-22 M. J. Martins

We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary…

Mathematical Physics · Physics 2016-08-09 Sabina Alazzawi , Gandalf Lechner

The reflection operators are the simplest examples of the non-local integrals of motion, which appear in many interesting problems in integrable CFT. For the so-called Fateev, quantum AKNS, paperclip and KdV integrable structures, they are…

High Energy Physics - Theory · Physics 2020-02-11 Gleb A. Kotousov , Sergei L. Lukyanov

We review recent progress towards the solution of exactly solved isotropic vertex models with arbitrary toroidal boundary conditions. Quantum space transformations make it possible the diagonalization of the corresponding transfer matrices…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 M. J. Martins

In this work we demonstrate a simple way to implement the quantum inverse scattering method to find eigenstates of spin-1/2 XXX Gaudin magnets in an arbitrarily oriented magnetic field. The procedure differs vastly from the most natural…

Mathematical Physics · Physics 2017-08-07 Alexandre Faribault , Hugo Tschirhart

We construct the Drinfeld twists (factorizing $F$-matrices) for the supersymmetric t-J model. Working in the basis provided by the $F$-matrix (i.e. the so-called $F$-basis), we obtain completely symmetric representations of the monodromy…

Statistical Mechanics · Physics 2009-11-10 Wen-Li Yang , Yao-Zhong Zhang , Shao-You Zhao

We propose a novel quantum integrable model for every non-simply laced simple Lie algebra ${\mathfrak g}$, which we call the folded integrable model. Its spectra correspond to solutions of the Bethe Ansatz equations obtained by folding the…

Quantum Algebra · Mathematics 2024-10-30 Edward Frenkel , David Hernandez , Nicolai Reshetikhin

We develop a unified formulation of the quantum inverse scattering method for lattice vertex models associated to the non-exceptional $A^{(2)}_{2r}$, $A^{(2)}_{2r-1}$, $B^{(1)}_r$, $C^{(1)}_r$, $D^{(1)}_{r+1}$ and $D^{(2)}_{r+1}$ Lie…

solv-int · Physics 2009-10-31 M. J. Martins

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such models can be expressed in terms of a bilinear combination of their highest coefficients. We obtain various…

Mathematical Physics · Physics 2015-09-07 S. Belliard , S. Pakuliak , E. Ragoucy , N. A. Slavnov

We construct integrable generalised models in a systematic way exploring different representations of the gl(N) algebra. The models are then interpreted in the context of atomic and molecular physics, most of them related to different types…

Strongly Correlated Electrons · Physics 2010-10-27 A. Foerster , E. Ragoucy

The exact solutions of the $D^{(1)}_3$ model (or the $so(6)$ quantum spin chain) with either periodic or general integrable open boundary conditions are obtained by using the off-diagonal Bethe Ansatz. From the fusion, the complete operator…

Mathematical Physics · Physics 2022-12-27 Guang-Liang Li , Junpeng Cao , Panpan Xue , Kun Hao , Pei Sun , Wen-Li Yang , Kangjie Shi , Yupeng Wang

Inverse iteration is known to be an effective method for computing eigenvectors corresponding to simple and well-separated eigenvalues. In the non-symmetric case, the solution of shifted Hessenberg systems is a central step. Existing…

Mathematical Software · Computer Science 2021-01-14 Angelika Schwarz

We study an integrable vertex model with a periodic boundary condition associated with U_q(A_n^{(1)}) at the crystallizing point q=0. It is an (n+1)-state cellular automaton describing the factorized scattering of solitons. The dynamics…

Quantum Algebra · Mathematics 2010-01-31 Atsuo Kuniba , Taichiro Takagi

Consider a tensor product of finite-dimensional irreducible gl_{N+1}-modules and its decomposition into irreducible modules. The gl_{N+1} Gaudin model assigns to each multiplicity space of that decomposition a commutative (Bethe) algebra of…

Quantum Algebra · Mathematics 2009-10-27 E. Mukhin , V. Tarasov , A. Varchenko

We establish the method of Bethe ansatz for the XXZ type model obtained from the R-matrix associated to quantum toroidal gl(1). We do that by using shuffle realizations of the modules and by showing that the Hamiltonian of the model is…

Quantum Algebra · Mathematics 2015-02-26 B. Feigin , M. Jimbo , T. Miwa , E. Mukhin

We compare two different methods of computing form factors. One is the well established procedure of solving the form factor consistency equations and the other is to represent the field content as well as the particle creation operators in…

High Energy Physics - Theory · Physics 2011-04-20 O. A. Castro-Alvaredo , A. Fring