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Related papers: Spinorial R operator and Algebraic Bethe Ansatz

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We show that eigenvalues of the family of Baxter Q-operators for supersymmetric integrable spin chains constructed with the gl(K|M)-invariant $R$-matrix obey the Hirota bilinear difference equation. The nested Bethe ansatz for super spin…

High Energy Physics - Theory · Physics 2008-11-26 Vladimir Kazakov , Alexander Sorin , Anton Zabrodin

The algebraic structure of the 1D Hubbard model is studied by means of the fermionic R-operator approach. This approach treats the fermion models directly in the framework of the quantum inverse scattering method. Compared with the graded…

Statistical Mechanics · Physics 2009-10-31 Yukiko Umeno

We consider open XXX spins chain with two general boundary matrices submitted to one constraint, which is equivalent to the possibility to put the two matrices in a triangular form. We construct Bethe vectors from a generalized algebraic…

Mathematical Physics · Physics 2015-06-11 S. Belliard , N. Crampe , E. Ragoucy

We examine the Onsager algebra symmetry of $\tau^{(j)}$-matrices in the superintegrable chiral Potts model. The comparison of Onsager algebra symmetry of the chiral Potts model with the $sl_2$-loop algebra symmetry of six-vertex model at…

Statistical Mechanics · Physics 2007-05-23 Shi-shyr Roan

We describe the Algebraic Bethe Ansatz for the spin-1/2 XXX and XXZ Heisenberg chains with open and periodic boundary conditions in terms of tensor networks. These Bethe eigenstates have the structure of Matrix Product States with a…

Strongly Correlated Electrons · Physics 2012-07-23 Valentin Murg , Vladimir E. Korepin , Frank Verstraete

We study the highest weight representations of the RTT algebras for the R matrix of sp_q(2n) type by the nested algebraic Bethe ansatz. It is a generalization of our study for R matrix of sp(2n) and so(2n) type

Mathematical Physics · Physics 2020-10-28 C. Burdik , O. Navratil

We study the trigonometric quantum spin-Calogero-Sutherland model, and the Haldane-Shastry spin chain as a special case, using a Bethe-ansatz analysis. We harness the model's Yangian symmetry to import the standard tools of integrability…

Mathematical Physics · Physics 2025-03-27 Gwenaël Ferrando , Jules Lamers , Fedor Levkovich-Maslyuk , Didina Serban

Yang-Baxter R operators symmetric with respect to the orthogonal and symplectic algebras are considered in an uniform way. Explicit forms for the spinorial and metaplectic R operators are obtained. L operators, obeying the RLL relation with…

Mathematical Physics · Physics 2016-02-17 A. P. Isaev , D. Karakhanyan , R. Kirschner

A general method is proposed for constructing the Bethe ansatz equations of integrable models without U(1) symmetry. As an example, the exact spectrum of the XXZ spin ring with M{\" o}bius like topological boundary condition is derived by…

Statistical Mechanics · Physics 2015-06-16 Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

We give a brief review on the use of Bethe ansatz techniques to construct solutions of recursive functional equations which emerged in a bootstrap approach to the quantum Ernst system. The construction involves two particular limits of a…

Mathematical Physics · Physics 2009-10-31 M. Niedermaier , H. Samtleben

A new method is introduced to derive general recurrence relations for off-shell Bethe vectors in quantum integrable models with either type $\mathfrak{gl}_n$ or type $\mathfrak{o}_{2n+1}$ symmetries. These recurrence relations describe how…

Quantum Algebra · Mathematics 2025-09-23 Andrii Liashyk , Stanislav Pakuliak , Eric Ragoucy

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

We consider quantum graphs with spin-orbit couplings at the vertices. Time-reversal invariance implies that the bond S-matrix is in the orthogonal or symplectic symmetry class, depending on spin quantum number s being integer or…

Chaotic Dynamics · Physics 2010-12-06 Jens Bolte , Jonathan Harrison

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

In integrable spin chains, the spectral problem can be solved by the method of Bethe ansatz, which transforms the problem of diagonalization of the Hamiltonian into the problem of solving a set of algebraic equations named Bethe equations.…

High Energy Physics - Theory · Physics 2025-08-27 Yi-Jun He , Jue Hou , Yi-Chao Liu , Zi-Xi Tan

We investigate form factors of local operators in the multi-component Quantum Non-linear Schr\"odinger model, a prototype theory solvable by the so-called nested Bethe Ansatz. We determine the analytic properties of the infinite volume form…

Statistical Mechanics · Physics 2015-06-04 Balazs Pozsgay , Willem-Victor van Gerven Oei , Marton Kormos

A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…

Atomic Physics · Physics 2009-11-10 G. Gaigalas , Z. Rudzikas , C. Froese Fischer

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 construct the exact spectral parameter dependent vertex R-matrix for the classical 3D $\mathcal{N}$-state chiral Potts models, convenient for considering the model in context of the Bethe ansatz. The R-matrix is defined on the…

Mathematical Physics · Physics 2022-01-19 Sh. Khachatryan , A. Sedrakyan

We extend the results of spin ladder models associated with the Lie algebras $su(2^n)$ to the case of the orthogonal and symplectic algebras $o(2^n),\ sp(2^n)$ where n is the number of legs for the system. Two classes of models are found…

Statistical Mechanics · Physics 2009-10-31 M. T. Batchelor , J. de Gier , J. Links , M. Maslen