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Related papers: Baxter Q-operator for graded SL(2|1) spin chain

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In this paper, we look at the asymmetric simple exclusion process with open boundaries with a current-counting deformation. We construct a two-parameter family of transfer matrices which commute with the deformed Markov matrix of the…

Mathematical Physics · Physics 2014-07-11 Alexandre Lazarescu , Vincent Pasquier

We construct the Baxter's operator and the corresponding Baxter's equation for a quantum version of the Ablowitz Ladik model. The result is achieved by looking at the quantum analogue of the classical Backlund transformations. For…

Mathematical Physics · Physics 2015-08-10 Federico Zullo

We consider integrable vertex models whose Boltzmann weights (R-matrices) are trigonometric solutions to the graded Yang-Baxter equation. As is well known the latter can be generically constructed from quantum affine superalgebras…

Statistical Mechanics · Physics 2008-11-26 Christian Korff , Itzhak Roditi

Taking the isotropic limit in a recent representation theoretic construction of Baxter's Q-operators for the XXZ model with quasi-periodic boundary conditions we obtain new results for the XXX model. We show that quasi-periodic boundary…

Mathematical Physics · Physics 2009-11-11 Christian Korff

We introduce a $Q$-operator $\mathcal{Q}_z$ for the hyperbolic Calogero--Moser system as a one-parameter family of explicit integral operators. We establish the standard properties of a $Q$-operator, i.e.~invariance of Hamiltonians,…

Mathematical Physics · Physics 2023-11-08 Martin Hallnäs

We obtain Gauss-Givental integral representation for the eigenfunctions of quantum Toda chain with boundary interaction of BC type. For this we introduce reflection operator satisfying reflection equation with DST chain Lax matrices.…

Mathematical Physics · Physics 2026-03-20 N. Belousov , S. Derkachov , S. Khoroshkin

For the class of quantum integrable models generated from the $q-$Onsager algebra, a basis of bispectral multivariable $q-$orthogonal polynomials is exhibited. In a first part, it is shown that the multivariable Askey-Wilson polynomials…

Mathematical Physics · Physics 2018-02-01 Pascal Baseilhac , Xavier Martin

We investigate an N-state spin model called quantum relativistic Toda chain and based on the unitary finite dimensional representations of the Weyl algebra with q being N-th primitive root of unity. Parameters of the finite dimensional…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 S. Pakuliak , S. Sergeev

We study solutions of the Yang-Baxter equation on a tensor product of an arbitrary finite-dimensional and an arbitrary infinite-dimensional representations of the rank one symmetry algebra. We consider the cases of the Lie algebra sl_2, the…

Mathematical Physics · Physics 2015-03-02 D. Chicherin , S. Derkachov

We propose a basis for rational gl(N) spin chains in an arbitrary rectangular representation $(S^A)$ that factorises the Bethe vectors into products of Slater determinants in Baxter Q-functions. This basis is constructed by repeated action…

Mathematical Physics · Physics 2020-03-11 Paul Ryan , Dmytro Volin

Each quantum superalgebra is a quasi-triangular Hopf superalgebra, so contains a \textit{universal $R$-matrix} in the tensor product algebra which satisfies the Yang-Baxter equation. Applying the vector representation $\pi$, which acts on…

Quantum Algebra · Mathematics 2016-09-07 K. A. Dancer , M. D. Gould , J. Links

We demonstrate that the Q matrix introduced in Baxter's 1972 solution of the eight vertex model has some eigenvectors which are not eigenvectors of the spin reflection operator and conjecture a new functional equation for Q(v) which both…

Statistical Mechanics · Physics 2007-05-23 Klaus Fabricius , Barry M. McCoy

Using the algebraic Bethe ansatz method, and the solution of the quantum inverse scattering problem for local spins, we obtain multiple integral representations of the $n$-point correlation functions of the XXZ Heisenberg spin-$1 \over 2$…

Mathematical Physics · Physics 2018-08-30 N. Kitanine , J. M. Maillet , V. Terras

In this paper we derive novel families of inclusion sets for the spectrum and pseudospectrum of large classes of bounded linear operators, and establish convergence of particular sequences of these inclusion sets to the spectrum or…

Spectral Theory · Mathematics 2024-06-11 Simon N. Chandler-Wilde , Ratchanikorn Chonchaiya , Marko Lindner

The spectral decomposition of regular Uq(sl_2)-invariant solutions of the Yang-Baxter equation is studied. An algorithm for finding all possible solutions of spin s is developed. It also allows to reconstruct the R-matrix from a given…

Quantum Algebra · Mathematics 2007-05-23 Andrei Bytsko

By using a variant of quantum inverse scattering method (QISM) which is directly applicable to field theoretical systems, we derive all possible commutation relations among the operator valued elements of the monodromy matrix associated…

High Energy Physics - Theory · Physics 2009-11-10 B. Basu-Mallick , Tanaya Bhattacharyya

Representations of quantum superalgebras provide a natural framework in which to model supersymmetric quantum systems. Each quantum superalgebra, belonging to the class of quasi-triangular Hopf superalgebras, contains a universal R-matrix…

Quantum Algebra · Mathematics 2016-09-07 K. A. Dancer , M. D. Gould , J. Links

We study a special class of operators T satisfying the transmutation relation (Tu)"-qTu=Tu" in the sense of distributions, where q is a locally integrable function, and u belongs to a suitable space of distributions depending on the…

Classical Analysis and ODEs · Mathematics 2016-12-05 Hugo M Campos

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

Condensed Matter · Physics 2016-08-31 J. Abad , M. Rios

Form factors for local spin operators of the XXZ Heisenberg spin-1/2 finite chain are computed. Representation theory of Drinfel'd twists for the sl2 quantum affine algebra in finite dimensional modules is used to calculate scalar products…

Mathematical Physics · Physics 2018-08-30 N. Kitanine , J. M. Maillet , V. Terras