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Related papers: Spinorial R operator and Algebraic Bethe Ansatz

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Extending the method proposed in [arXiv:1109.5524], we derive QQ-relations (functional relations among Baxter Q-functions) and T-functions (eigenvalues of transfer matrices) for fusion vertex models associated with the twisted quantum…

Mathematical Physics · Physics 2024-07-15 Zengo Tsuboi

We prove the modified algebraic Bethe Ansatz characterization of the spectral problem for the closed XXX Heisenberg spin chain with an arbitrary twist and arbitrary positive (half)-integer spin at each site of the chain. We provide two…

Mathematical Physics · Physics 2019-09-09 Samuel Belliard , Nikita A. Slavnov , Benoit Vallet

We consider supersymmetry algebras in space-times with arbitrary signature and minimal number of spinor generators. The interrelation between super Poincar\'e and super conformal algebras is elucidated. Minimal super conformal algebras are…

High Energy Physics - Theory · Physics 2009-10-31 R. D'Auria , S. Ferrara , M. A. Lledó , V. S. Varadarajan

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

We present the exact solution of a family of two-spins models. The models are solved by the algebraic Bethe ansatz method using the $gl(2)$-invariant $R$-matrix and a multi-spins Lax operator. The interactions are by the Heisenberg spins…

Mathematical Physics · Physics 2019-09-18 G. Santos

The tensorial form of the spin-other-orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off-diagonal matrix elements according to an approach, based…

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

For integrable inhomogeneous supersymmetric spin chains (generalized graded magnets) constructed employing Y(gl(N|M))-invariant R-matrices in finite-dimensional representations we introduce the master T-operator which is a sort of…

Mathematical Physics · Physics 2015-05-25 Zengo Tsuboi , Anton Zabrodin , Andrei Zotov

We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression…

Mathematical Physics · Physics 2014-10-23 N. Cirilo António , N. Manojlović , I. Salom

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

A chiral coordinate Bethe ansatz method is developed to study the periodic XYZ chain. We construct a set of chiral vectors with fixed number of kinks. All vectors are factorized and have simple structures. Under roots of unity conditions,…

Statistical Mechanics · Physics 2024-03-21 Xin Zhang , Andreas Klümper , Vladislav Popkov

The eigenvectors of the Hamiltonian ${\cal H}_{N}$ of $N$-sites quantum spin chains with elliptic exchange are connected with the double Bloch meromorphic solutions of the quantum continuous elliptic Calogero-Moser problem. This fact allows…

Mathematical Physics · Physics 2007-05-23 V. I. Inozemtsev

In this paper we clarify the relationship between inhomogeneous quantum spin chains and classical integrable many-body systems. It provides an alternative (to the nested Bethe ansatz) method for computation of spectra of the spin chains.…

High Energy Physics - Theory · Physics 2015-06-17 A. Gorsky , A. Zabrodin , A. Zotov

The algebraic Bethe ansatz can be performed rather abstractly for whole classes of models sharing the same $R$-matrix, the only prerequisite being the existence of an appropriate pseudo vacuum state. Here we perform the algebraic Bethe…

Statistical Mechanics · Physics 2017-08-16 Frank Göhmann , Alexander Seel

We study Yang-Baxter equations with orthosymplectic supersymmetry. We extend a new approach of the construction of the spinor and metaplectic $\hat{\cal R}$-operators with orthogonal and symplectic symmetries to the supersymmetric case of…

Mathematical Physics · Physics 2021-03-17 A. P. Isaev , D. Karakhanyan , R. Kirschner

We obtain determinant representations for the form factors of the monodromy matrix entries in quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $GL(3)$-invariant $R$-matrix. These representations can be…

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

We consider the quantum integrable spin chain models associated with the Jimbo R-matrix based on the quantum affine algebra $D^{(2)}_{n+1}$, subject to quantum-group-invariant boundary conditions parameterized by two discrete variables…

High Energy Physics - Theory · Physics 2025-12-19 Holger Frahm , Sascha Gehrmann , Rafael I. Nepomechie , Ana L. Retore

The general expression for the local matrix $t(\theta)$ of a quantum chain with the site space in any representation of su(3) is obtained. This is made by generalizing $t(\theta)$ from the fundamental representation and imposing the…

Condensed Matter · Physics 2016-08-15 J. Abad , M. Ríos

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 review some of the strategies that can be implemented to infer an $R$-matrix from the knowledge of its Hamiltonian. We apply them to the classification achieved in arXiv:1306.6303, on three state $U(1)$-invariant Hamiltonians solvable by…

Mathematical Physics · Physics 2015-06-19 T. Fonseca , L. Frappat , E. Ragoucy

We describe a simple quantum mechanical method that can be used to obtain accurate numerical results over long time scales for the spin correlation tensor of an electron spin that is hyperfine coupled to a large number of nuclear spins.…

Quantum Physics · Physics 2018-08-13 Lachlan P. Lindoy , David E. Manolopoulos